Robust cooperative control method for surface-underwater vehicle with limited communication

Abstract

The application discloses a kind of water surface-underwater vehicle cooperative robust control method considering communication restriction, comprising, the kinematic model and dynamics model of USV and UUV are established;Adopt master-slave cooperative architecture, define UUV track virtual ship, USV track UUV;Improved adaptive LVS guidance law is generated by introducing atan2 function design guidance signal;Based on the dynamics model, an adaptive segmented boundary compensation method is designed;Based on guidance signal and fusion output, virtual control law and actual control law are designed using backstepping method;Nonlinear attenuation law is constructed, adaptive offset driven by tracking error is introduced, and improved integral dynamic event triggering mechanism is designed under the condition of communication restriction to determine the speed command and rudder angle command;Introducing actuator gain compensation coefficient, designing actuator mapping and saturation processing, generating final control command;The application realizes the master-slave cooperative path tracking control of virtual ship guiding UUV and UUV guiding USV.

Description

Technical Field

[0001] This invention relates to the field of cooperative control technology for marine robots, and more particularly to a robust cooperative control method for surface-underwater vehicles considering communication limitations. Background Technology

[0002] In the field of ship motion control, path tracking is a core issue in achieving autonomous navigation. Ship dynamics typically exhibit complex characteristics such as large inertia, strong nonlinearity, and significant time delays, posing a continuous challenge to the design of high-precision path tracking controllers.

[0003] Currently, research on path tracking control for surface-underwater (USV-UUV) cross-domain cooperative systems is still in the exploratory stage, facing numerous theoretical and engineering challenges. Existing technologies are mostly adapted from the surface-air (USV-UAV) cooperative control framework, failing to fully consider the essential differences between USVs and UUVs in terms of dynamic characteristics, motion space, and environmental disturbance modes, resulting in significant shortcomings when applied in actual marine environments.

[0004] At the guidance system level, mainstream LVS guidance methods have two key drawbacks. First, traditional LVS guidance laws use the arctangent function to calculate the desired course. When the lateral error is large or the drift angle approaches a specific value, singularity problems arise, threatening the stability of the closed-loop system. Second, there is a lack of effective online estimation and compensation mechanisms for time-varying ocean environmental disturbances. When there is a constant or slowly varying lateral current, the controlled vessel will generate steady-state tracking errors; under time-varying, non-uniform disturbances, dynamic tracking errors increase significantly, especially during changes in path curvature or waypoint switching phases, which may cause significant trajectory oscillations or deviations.

[0005] At the control system level, to address the inherent strong nonlinearity, coupling, and model uncertainty in USV and UUV models, existing research widely employs function approximation techniques such as radial basis function neural networks and fuzzy logic systems for online compensation. While these methods can theoretically approximate unknown nonlinear functions with arbitrary precision, the large number of adaptive parameters they introduce, such as weights, center, and width, drastically increases the controller's design dimensionality and online computational burden. Furthermore, traditional single fixed boundary compensation methods are highly conservative and struggle to adapt to changes in nonlinear characteristics under different speeds and operating conditions, leading to controller performance degradation or excessive control input under certain conditions.

[0006] At the event triggering mechanism level, most existing integral-based event triggering schemes use fixed threshold parameters, which cannot dynamically adjust the trigger sensitivity according to the system state and disturbance intensity. When the disturbance increases or the system is in a dynamic process, the fixed threshold may lead to untimely triggering and loss of control performance; during the stable operation phase of the system, unnecessary triggering may waste communication resources. In addition, the tuning of the fixed threshold requires a lot of trial and error, making it difficult to achieve the optimal balance between performance and resource consumption under different task scenarios.

[0007] At the level of system integration and robustness, existing cooperative control schemes often design guidance, control, and drive modules relatively independently, with insufficient consideration for the dynamic characteristics of the servo system and the physical constraints of the actuators. They typically use simple saturation functions for post-processing, which may lead to performance degradation or even instability of the closed-loop system near the constraint boundaries. Furthermore, for the heterogeneous hybrid-order system of USV-UUV, controller design usually requires different control structures for each component and cumbersome coordination, lacking a unified, concise, and easily stable integrated design framework.

[0008] In summary, existing USV-UUV cooperative path tracking control technologies suffer from the following core deficiencies that urgently need to be addressed: 1) The guidance strategy has singularity and insufficient anti-disturbance: The traditional LVS guidance law has singularity problems under large drift angles and lacks an effective adaptive drift angle compensation mechanism, which leads to a decrease in tracking accuracy in complex environments.

[0009] 2) Nonlinear approximation methods are highly conservative and computationally complex: relying on complex neural network approximators leads to numerous adaptive parameters, making debugging difficult and computationally burdensome; while fixed boundary compensation methods are also highly conservative and difficult to adapt to different working conditions.

[0010] 3) Poor adaptability of event triggering mechanism: Fixed threshold integral event triggering cannot dynamically adapt to changes in system state and disturbances, making it difficult to maximize the reduction of communication load while ensuring control accuracy. Summary of the Invention

[0011] This invention provides a robust cooperative control method for surface-underwater vehicles that takes into account communication limitations, in order to overcome the aforementioned technical problems.

[0012] To achieve the above objectives, the technical solution of the present invention is as follows: A robust cooperative control method for surface-underwater vehicles considering communication constraints includes: S1: Establish kinematic and dynamic models for USV and UUV. The kinematic model is used to describe the relationship between the vehicle's velocity in the attached coordinate system and its attitude change rate in the geodetic coordinate system. The dynamic model is used to describe the relationship between the resultant force on the vehicle and its acceleration. S2: A master-slave collaborative architecture is adopted, defining the UUV as the first-level follower tracking the virtual ship and the USV as the second-level follower tracking the UUV; an atan2 function is introduced, and based on the kinematic model and the atan2 function, an improved adaptive LVS guidance law is designed. The improved adaptive LVS guidance law is used to compensate for the lateral drift caused by environmental disturbances online according to the position tracking error between the vehicle and the target and the introduced adaptive drift angle estimation term, so as to generate an improved guidance signal. S3: Based on the dynamic model, an adaptive segmented boundary compensation method is designed. The compensation method is used to softly divide the operating state space of the vehicle and use regression vectors of different complexities in each sub-region after division. The fusion output is generated by weighted fusion to approximate the unknown nonlinear dynamic terms in the system online. S4: Based on the guidance signal and the fusion output, a virtual control law and an actual control law are designed using the backstepping method. The virtual control law is used to calculate the desired speed based on the position error and heading angle error, and then define the speed error. The actual control law is used to calculate the desired control torque based on the speed tracking error and the fusion output. S5: Construct a nonlinear decay law and introduce an adaptive offset driven by the tracking error. Based on the dynamic gain controlled by the nonlinear decay law and the adaptive offset, a dynamic threshold is formed. Under communication-limited conditions, an improved integral dynamic event triggering mechanism is designed. The integral dynamic event triggering mechanism is used to determine the speed command and rudder angle command according to the dynamic threshold and decide whether to update the control command of the actuator. S6: Introduce actuator gain compensation coefficient, design actuator mapping and saturation processing to convert the desired control torque into propeller speed command and rudder angle command; after the event trigger judgment is passed, the command is physically limited to generate the final control command to realize master-slave cooperative path tracking control of virtual ship guiding UUV and UUV guiding USV.

[0013] Furthermore, kinematic and dynamic models of USV and UUV are established, including: S11. Construct the kinematic models of USV and UUV, with the following formulas:

[0014] The pose of the USV in the geodetic coordinate system is: , Indicates location, The velocity vector in the attached coordinate system represents the heading angle. ,in For oscillation speed, For sway speed, The bow roll rate is ; the UUV's pose is . The velocity vector is ; They represent USV and UUV respectively; Let be a rotation matrix, and its expression is:

[0015]

[0016] S12. Construct the dynamic models of USV and UUV, with the following formulas:

[0017] in, The inertia matrix includes the added mass. and These represent the Coriolis-centripetal force matrix and the damping matrix, respectively. Indicates a bounded environmental disturbance; The actual control law to be designed; The term without external force is reduced to a scalar function, and its formula is:

[0018] in, , , It is a scalar function, i.e., a nonlinear dynamic term; The dynamic equations of USV and UUV in component form based on scalar functions are as follows: .

[0019] Furthermore, a master-slave collaborative architecture is adopted, defining the UUV as the first-level follower tracking the virtual vessel, and the USV as the second-level follower tracking the UUV; an atan2 function is introduced, and based on the kinematic model and the atan2 function, an improved adaptive LVS guidance law is designed. This improved adaptive LVS guidance law is used to compensate online for lateral drift caused by environmental disturbances based on the position tracking error between the vehicle and the target and the introduced adaptive drift angle estimation term, in order to generate an improved guidance signal, including: S21. Based on the master-slave collaborative architecture, calculate the position tracking error of the UUV relative to the virtual ship and the position tracking error of the USV relative to the UUV, using the following formulas:

[0020]

[0021] in, , Indicates the actual position coordinates of the USV; , Indicates the actual location coordinates of the UUV; This represents the position tracking error of the UUV relative to the virtual ship. This indicates the position tracking error of the USV relative to the UUV; The coordinates of the virtual ship's desired position; and These represent the straight-line distance from the UUV to the virtual ship and the straight-line distance from the USV to the UUV, respectively. S22. Based on the aforementioned position tracking error, an improved guidance signal is designed for each aircraft, and its formula is as follows:

[0022] in, For improved guidance signals, for function, This is the adaptive drift angle estimation term; S23. Design the update law for the adaptive drift angle estimation term, the formula of which is:

[0023] in, For adaptive gain; This represents the expected heading angle of the UUV tracked by the USV. This represents the expected heading angle of the virtual ship being tracked by the UUV; ; This refers to the heading angle tracking error.

[0024] Furthermore, based on the aforementioned dynamic model, an adaptive segmented boundary compensation method is designed. This compensation method is used to softly partition the operational state space of the vehicle, and within each partitioned sub-region, regression vectors of different complexities are used to generate a fused output through weighted fusion, in order to approximate the unknown nonlinear dynamics in the system online, including: S31. Define the velocity norm vector of the aircraft. ,Will The space is divided into three centers The membership degree is calculated using the Gaussian kernel function, and the formula is as follows:

[0025] in, It is a constant used to control the kernel width. Membership degree; Normalize the membership degrees to obtain normalized weights, the formula of which is:

[0026] satisfy ; S32. Within each central region, construct a polynomial regression vector of increasing order, with the following formula:

[0027] S33. The fusion output of the sway and pitch channels is constructed based on the polynomial regression vector and normalized weights, and the formulas are as follows:

[0028] in, For the fusion output of the oscillating channel, For the fusion output of the bow rocker channel, and Let be the optimal parameter vector to be estimated; Design an online adaptive law for the sway and yaw channels to estimate the optimal parameter vector, the formula of which is:

[0029] in, and The speed tracking error to be solved is... To design gain.

[0030] Furthermore, based on the guidance signal and the fused output, a virtual control law and an actual control law are designed using the backstepping method. The virtual control law is used to calculate the desired velocity based on the position error and heading angle error, and then define the velocity error. The actual control law is used to calculate the desired control torque based on the velocity tracking error and the fused output, including: S41. Based on the kinematic model, derive the derivatives of the position tracking error and the heading angle tracking error. The formula is as follows:

[0031] The virtual control law is designed to stabilize the tracking error, and its formula is as follows:

[0032] in, and These are the virtual control laws for the sway channel and the yaw channel, respectively, and numerically they are the expected reference values ​​for the sway velocity and yaw angular velocity. For design parameters, This is a time-varying offset term; this term regularizes the error along the flight path to ensure... The heading angle tracking error satisfies the following constraints:

[0033] S42. A first-order instruction filter is used to filter the virtual control law. The formula is as follows:

[0034] in, It is a time constant. and The virtual control law after filtering; filter error and The following constraints must be met:

[0035] in, The term is a known bounded perturbation. S43. Define the speed tracking error, and its formula is:

[0036] Differentiating it, the formula is:

[0037] in, and For the sway and yaw channels, the inertia coefficients are denoted as . S44. Based on the derivative of the speed tracking error and the fused output, the unknown nonlinear function in the dynamic model is compensated, and the actual control law is designed. The formula is as follows:

[0038] in, To design gain, and These are the actual control laws for the sway channel and the yaw channel, respectively, which are numerically equivalent to the desired control torque.

[0039] Furthermore, a nonlinear decay law is constructed, and an adaptive offset driven by tracking error is introduced. Based on the dynamic gain controlled by the nonlinear decay law and the adaptive offset, a dynamic threshold is jointly formed. Under communication-constrained conditions, an improved integral dynamic event triggering mechanism is designed. This mechanism is used to determine whether to update the control commands of the actuator based on the dynamic threshold, including: S51. Construct a nonlinear decay law, the formula of which is:

[0040]

[0041] An adaptive offset driven by the tracking error is introduced, based on a dynamic threshold jointly formed by the dynamic gain controlled by the nonlinear decay law and the adaptive offset, the formula of which is:

[0042] in, , For dynamic gain, and It is a nonlinear decay law. and For adaptive offset, For design parameters; S52. Define the generalized thrust-related variable as a piecewise constant signal, which at the trigger time... The update remains unchanged between two triggers, and its formula is:

[0043] in, Represents the generalized thrust-related variables. Indicates the propeller speed command. This is the rudder angle command; S53. Based on the dynamic threshold jointly constituted by the dynamic gain controlled by the nonlinear attenuation law and the adaptive offset, under communication-limited conditions, an integral event triggering condition is designed to determine the next triggering moment. The trigger condition is defined by the following formula: .

[0044] Furthermore, an actuator gain compensation coefficient is introduced, and actuator mapping and saturation processing are designed to convert the desired control torque into propeller speed commands and rudder angle commands. After the event trigger determination is passed, the commands are physically limited to generate the final control commands, including: S61. To compensate for uncertain actuator gain, an actuator gain compensation coefficient is introduced. and And design its adaptive law, the formula of which is:

[0045]

[0046] in, For design parameters; and Initial value; S62. Upon reaching the trigger moment, based on the actuator gain compensation coefficient, the actual control law is converted into propeller speed command and rudder angle command, with the following formula:

[0047] S63. When the triggering condition of an integral event is met, the next triggering time is reached. ， The speed command for the current control cycle and rudder angle commands Updated to control commands of the actual actuator and and in The instruction remains unchanged; when the triggering condition is not met, the actuator maintains the instruction value executed at the previous triggering time. S64. Apply saturation constraints to the propeller speed command and rudder angle command to satisfy the following conditions:

[0048] in, and These are the maximum allowable values ​​for propeller speed and rudder angle, respectively, and the command after saturation constraint is used as the input for the integral event triggering condition in S5.

[0049] Beneficial effects: This invention provides a robust cooperative control method for surface-underwater vehicles considering communication limitations, which has the following advantages: 1. This invention achieves a significant improvement in guidance robustness and safety: based on The improved adaptive LVS guidance law design solves the singularity problem of traditional LVS guidance under large drift angles. Combined with the adaptive drift angle compensation mechanism, it significantly improves the individual path tracking accuracy of USV and UUV in complex marine environments, laying a solid foundation for collaborative missions. 2. This invention achieves a balance between nonlinear approximation accuracy and efficiency: In the design process of the adaptive piecewise boundary compensation method, by softly partitioning the state space and using regression vectors of increasing order, the number of adaptive parameters is significantly reduced while the conservatism of traditional fixed boundary compensation is significantly reduced, thus achieving a good balance between approximation accuracy and computational efficiency. 3. The communication efficiency of the present invention is further improved: The improved integral dynamic event triggering mechanism of the present invention achieves online adaptive adjustment of triggering sensitivity through the combination of dynamic gain and adaptive offset. Under the premise of ensuring control performance, it minimizes the communication load from the controller to the actuator and extends the service life of the equipment. Attached Figure Description

[0050] 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.

[0051] Figure 1 A flowchart of the cooperative robust control method for surface-underwater vehicles considering communication limitations provided by the present invention; Figure 2 A framework diagram of a surface and underwater vessel collaborative control system is provided for this invention. Figure 3 This is a diagram of the adaptive LVS guidance framework provided by the present invention; Figure 4 This is a schematic diagram comparing the tracking results obtained by the nonlinear approximation method and the event triggering mechanism in an embodiment of the present invention; Figure 5 This is a schematic diagram showing the comparison results of the tracking errors obtained by the nonlinear approximation method and the event triggering mechanism in the embodiments of the present invention; Figure 6 This is a simulation diagram of a three-dimensional (3D) water surface and underwater vehicle cooperative system in an embodiment of the present invention; Figure 7 This is a schematic diagram of the positioning and attitude error of the cooperative system in an embodiment of the present invention; Figure 8 This is a schematic diagram of the USV propeller speed and rudder angle control input in an embodiment of the present invention; Figure 9 This is a schematic diagram of the UUV propeller speed and rudder angle control input in an embodiment of the present invention; Figure 10 This is a schematic diagram of the USV triggering interval in an embodiment of the present invention; Figure 11 This is a schematic diagram of the UUV triggering interval in an embodiment of the present invention. Detailed Implementation

[0052] 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.

[0053] This embodiment provides a robust cooperative control method for surface-underwater vehicles that considers communication limitations, such as... Figure 1 and Figure 2 As shown, it includes: S1: Establish kinematic and dynamic models for USV and UUV. The kinematic model is used to describe the relationship between the vehicle's velocity in the attached coordinate system and its attitude change rate in the geodetic coordinate system. The dynamic model is used to describe the relationship between the resultant force on the vehicle and its acceleration. S2: A master-slave collaborative architecture is adopted, defining the UUV as the first-level follower tracking the virtual ship and the USV as the second-level follower tracking the UUV; an atan2 function is introduced, and based on the kinematic model and the atan2 function, an improved adaptive LVS guidance law is designed. The improved adaptive LVS guidance law is used to compensate for the lateral drift caused by environmental disturbances online according to the position tracking error between the vehicle and the target and the introduced adaptive drift angle estimation term, so as to generate an improved guidance signal. S3: Based on the dynamic model, an adaptive segmented boundary compensation method is designed. The compensation method is used to softly divide the operating state space of the vehicle and use regression vectors of different complexities in each sub-region after division. The fusion output is generated by weighted fusion to approximate the unknown nonlinear dynamic terms in the system online. S4: Based on the guidance signal and the fusion output, a virtual control law and an actual control law are designed using the backstepping method. The virtual control law is used to calculate the desired speed based on the position error and heading angle error, and then define the speed error. The actual control law is used to calculate the desired control torque based on the speed tracking error and the fusion output. S5: Construct a nonlinear decay law and introduce an adaptive offset driven by the tracking error. Based on the dynamic gain controlled by the nonlinear decay law and the adaptive offset, a dynamic threshold is formed. Under communication-limited conditions, an improved integral dynamic event triggering mechanism is designed. The integral dynamic event triggering mechanism is used to determine the speed command and rudder angle command according to the dynamic threshold and decide whether to update the control command of the actuator. S6: Introduce actuator gain compensation coefficient, design actuator mapping and saturation processing to convert the desired control torque into propeller speed command and rudder angle command; after the event trigger judgment is passed, the command is physically limited to generate the final control command to realize master-slave cooperative path tracking control of virtual ship guiding UUV and UUV guiding USV.

[0054] This invention proposes an improved integrated guidance and adaptive event-triggered control scheme for USV-UUV cooperative systems, which mainly includes the following three core components: (1) Based on An improved adaptive LVS guidance law design is proposed to solve the singularity problem of traditional LVS guidance under large drift angles, and an adaptive drift angle compensation term is introduced to improve the anti-disturbance capability.

[0055] (2) Adaptive segmented boundary compensation method design: the state space is softly divided into three operating regions by Gaussian membership function, and local approximation is performed by regression vectors of different orders to reduce the conservatism and computational complexity of nonlinear compensation.

[0056] (3) An improved integral dynamic event triggering mechanism is designed, which constructs a dynamic threshold consisting of a dynamic gain controlled by a nonlinear decay law and an adaptive offset driven by tracking error, thereby realizing online adaptive adjustment of trigger sensitivity.

[0057] In a specific embodiment, kinematic and dynamic models are established for the USV and UUV. The kinematic model describes the relationship between the vehicle's velocity in the attached coordinate system and its rate of change of attitude in the geodetic coordinate system. The dynamic model describes the relationship between the resultant force acting on the vehicle and its acceleration. S11. Construct the kinematic models of USV and UUV, with the following formulas:

[0058] The USV moves in the horizontal plane, and its pose in the geodetic coordinate system is: , Indicates location, The velocity vector in the attached coordinate system represents the heading angle. ,in For oscillation speed, For sway speed, The bow roll rate; the UUV also includes heave motion, and the UUV's pose is... The velocity vector is ; They represent USV and UUV respectively; Let be a rotation matrix, and its expression is:

[0059]

[0060] S12. Construct dynamic models for USVs and UUVs according to standard marine vehicle modeling methods. The formulas are as follows:

[0061] in, The inertia matrix includes the added mass. and These represent the Coriolis-centripetal force matrix and the damping matrix, respectively. Indicates a bounded environmental disturbance; The actual control law to be designed; To facilitate control design, terms without external forces are reduced to scalar functions, the formula of which is:

[0062] in, , , It is a scalar function, i.e., a nonlinear dynamic term; The dynamic equations of USV and UUV in component form based on scalar functions are as follows: .

[0063] In a specific embodiment, a master-slave cooperative architecture is adopted, defining the UUV as the first-level follower tracking the virtual vessel, and the USV as the second-level follower tracking the UUV. An atan2 function is introduced, and based on the kinematic model and the atan2 function, an improved adaptive LVS guidance law is designed. This improved adaptive LVS guidance law is used to compensate online for lateral drift caused by environmental disturbances based on the position tracking error between the vehicle and the target and the introduced adaptive drift angle estimation term. The scheme for generating an improved guidance signal is as follows: S21. Based on the master-slave collaborative architecture, calculate the position tracking error of the UUV relative to the virtual ship and the position tracking error of the USV relative to the UUV, using the following formulas:

[0064]

[0065] in, , Indicates the actual position coordinates of the USV; , Indicates the actual location coordinates of the UUV; This represents the position tracking error of the UUV relative to the virtual ship. This indicates the position tracking error of the USV relative to the UUV; The coordinates of the virtual ship's desired position; and These represent the straight-line distance from the UUV to the virtual ship and the straight-line distance from the USV to the UUV, respectively. S22, guidance frame such as Figure 3 As shown, the UUV directly tracks the virtual ship, and the USV tracks the UUV. Therefore, based on the position tracking error, an improved guidance signal is designed for each vehicle, and its formula is:

[0066] in, For improved guidance signals, for function, This is the adaptive drift angle estimation term; This function avoids the limitations of the traditional arctangent function. The singularity problem of time, and the ability to correctly determine the quadrant; S23. Design the update law for the adaptive drift angle estimation term, the formula of which is:

[0067] in, As an adaptive gain, this adaptive term can estimate and compensate for the drift angle caused by disturbances such as ocean currents online, significantly improving guidance accuracy; This represents the expected heading angle of the UUV tracked by the USV. This represents the expected heading angle of the virtual ship being tracked by the UUV; ; This refers to the heading angle tracking error.

[0068] In a specific embodiment, based on the dynamic model, an adaptive segmented boundary compensation method is designed. This compensation method is used to softly partition the vehicle's operational state space and, within each partitioned sub-region, employ regression vectors of varying complexity. A weighted fusion method is used to generate a fused output, thus approximating the unknown nonlinear dynamic terms in the system online. To avoid the conservatism of fixed robust boundaries, an adaptive piecewise approximation structure with soft partitioning is constructed. The specific steps are as follows: S31. Define the velocity norm vector of the aircraft. ,Will The space is divided into three centers The membership degree is calculated using the Gaussian kernel function, and the formula is as follows:

[0069] in, It is a constant used to control the kernel width. Membership degree; Normalize the membership degrees to obtain normalized weights, the formula of which is:

[0070] satisfy ; S32. Within each central region, construct a polynomial regression vector of increasing order, with the following formula:

[0071] S33. The fusion output of the sway and pitch channels is constructed based on the polynomial regression vector and normalized weights, and the formulas are as follows:

[0072] in, For the fusion output of the oscillating channel, For the fusion output of the bow rocker channel, and Let be the optimal parameter vector to be estimated; Design an online adaptive law for the sway and yaw channels to estimate the optimal parameter vector, the formula of which is:

[0073] in, and The speed tracking error to be solved is... To design the gain, a small positive number is usually chosen to ensure that the estimate is bounded.

[0074] This method uses explicitly constructed piecewise bounded functions and adaptive parameters to cover nonlinear terms, replacing the RBF neural network that requires extensive online parameter tuning. At the same time, it significantly reduces the conservatism of the compensation through soft partitioning and regression vectors with increasing order.

[0075] In a specific embodiment, based on the guidance signal and the fused output, a virtual control law and an actual control law are designed using the backstepping method. The virtual control law is used to calculate the desired velocity based on the position error and heading angle error, and then define the velocity error. The actual control law is used to calculate the desired control torque based on the velocity tracking error and the fused output. S41. Based on the kinematic model, derive the derivatives of the position tracking error and the heading angle tracking error. The formula is as follows:

[0076] The virtual control law is designed to stabilize the tracking error, and its formula is as follows:

[0077] in, and These are the virtual control laws for the sway channel and the yaw channel, respectively, and numerically they are the expected reference values ​​for the sway velocity and yaw angular velocity. For design parameters, This is a time-varying offset term; this term regularizes the error along the flight path, maintains a good virtual control state, and ensures... To avoid exist When singularities occur, the heading angle tracking error must satisfy the following constraints:

[0078] S42. To avoid the "computational explosion" problem caused by differentiating the virtual control law, a first-order instruction filter is used to filter the virtual control law. The formula is as follows:

[0079] in, It is a time constant. and The virtual control law after filtering; filter error and The following constraints must be met:

[0080] in, The term is a known bounded perturbation. S43. Define the speed tracking error, and its formula is:

[0081] Differentiating it, the formula is:

[0082] in, and For the sway and yaw channels, the inertia coefficients are denoted as . S44. Based on the derivative of the speed tracking error and the fused output, the unknown nonlinear function in the dynamic model is compensated, and the actual control law is designed. The formula is as follows:

[0083] in, To design gain, and These are the actual control laws for the sway channel and the yaw channel, respectively, which are numerically equivalent to the desired control torque.

[0084] In a specific embodiment, to reduce the communication load between the controller and the actuator, a nonlinear attenuation law is constructed, and an adaptive offset driven by the tracking error is introduced. Based on the dynamic gain controlled by the nonlinear attenuation law and the adaptive offset, a dynamic threshold is jointly formed. Under communication-constrained conditions, an improved integral dynamic event triggering mechanism is designed. This mechanism is used to determine whether to update the control command of the actuator based on the dynamic threshold, considering the speed command and rudder angle command. S51. Construct a nonlinear decay law, the formula of which is:

[0085]

[0086] An adaptive offset driven by the tracking error is introduced, based on a dynamic threshold jointly formed by the dynamic gain controlled by the nonlinear decay law and the adaptive offset, the formula of which is:

[0087] in, , For dynamic gain, and It is a nonlinear decay law. and For adaptive offset, For design parameters; S52. Define the generalized thrust-related variable as a piecewise constant signal, which at the trigger time... The update remains unchanged between two triggers, and its formula is:

[0088] in, Represents the generalized thrust-related variables. Indicates the propeller speed command. This is the rudder angle command; S53. Based on the dynamic threshold jointly constituted by the dynamic gain controlled by the nonlinear attenuation law and the adaptive offset, under communication-limited conditions, an integral event triggering condition is designed to determine the next triggering moment. The trigger condition is defined by the following formula: .

[0089] This mechanism achieves online adaptive adjustment of trigger sensitivity through nonlinearly decaying dynamic gain and adaptive offset driven by tracking error. When the system error is large or the disturbance is strong, the trigger frequency automatically increases to ensure control performance; when the system is running smoothly, the trigger frequency automatically decreases to save communication resources. At the same time, this mechanism fundamentally avoids the Zeno phenomenon.

[0090] In a specific embodiment, an actuator gain compensation coefficient is introduced, and actuator mapping and saturation processing are designed to convert the desired control torque into propeller speed commands and rudder angle commands. After the event trigger determination is passed, the commands are physically limited to generate the final control commands. The scheme for achieving master-slave cooperative path tracking control of virtual ship guiding UUV and UUV guiding USV is as follows: S61. To compensate for uncertain actuator gain, an actuator gain compensation coefficient is introduced. and And design its adaptive law, the formula of which is:

[0091]

[0092] in, For design parameters; and Initial value; S62. Upon reaching the trigger moment, based on the actuator gain compensation coefficient, the actual control law is converted into propeller speed command and rudder angle command, with the following formula:

[0093] S63. When the triggering condition of an integral event is met, the next triggering time is reached. ， The speed command for the current control cycle and rudder angle commands Updated to control commands of the actual actuator and and in The instruction remains unchanged; when the triggering condition is not met, the actuator maintains the instruction value executed at the previous triggering time. S64. In practical maritime applications, the maximum thrust generated by a propeller is limited by physical conditions. Furthermore, the rudder angle is typically constrained within a certain range. Therefore, the actual control command is defined as the propeller speed. and rudder angle Saturation constraints are applied to the propeller speed command and rudder angle command to ensure that they meet the following conditions:

[0094] in, and These are the maximum allowable values ​​for propeller speed and rudder angle, respectively, and the command after saturation constraint is used as the input for the integral event triggering condition in S5.

[0095] To verify the effectiveness of the method proposed in this invention, two sets of numerical experiments were conducted on the MATLAB simulation platform: a comparative experiment of nonlinear approximation methods and a comparative experiment of event triggering mechanisms.

[0096] Comparative Experiment 1 compares the adaptive segmented boundary compensation method with the traditional fixed boundary compensation method. Figure 4 The trajectory results of the two schemes were compared. The adaptive piecewise approximation method makes the ship closer to the target path, especially during speed changes, while the traditional bounded compensation technique shows significant deviations. Figure 5The corresponding orbital position error is shown to vary over time. The adaptive scheme converges faster and maintains a smaller steady-state error throughout the mission.

[0097] The results show that the adaptive piecewise approximation method can more accurately capture the changes in nonlinear characteristics under different speeds and operating conditions, and significantly reduce the amplitude and fluctuation of the control input while ensuring system stability. Furthermore, the number of adaptive parameters in this method is far fewer than that of the RBF neural network method, greatly reducing the online computational burden and the difficulty of parameter tuning.

[0098] Comparative Experiment 2 compares the improved dynamic threshold integral event triggering mechanism with the traditional fixed threshold integral event triggering mechanism. While maintaining the same tracking accuracy, the improved IDTM dynamically adjusts the triggering frequency based on the system state and disturbance intensity. When the system is undergoing dynamic changes, the triggering frequency is appropriately increased to respond quickly to disturbances; when the system is running smoothly, the triggering frequency is significantly reduced. Simulation results show that, compared to the fixed threshold ITM, the improved IDTM effectively extends the average triggering interval, thereby further reducing communication load and actuator wear. Furthermore, a strict positive lower bound exists between consecutive triggering events, verifying that the proposed IDTM successfully eliminates the Zeno phenomenon.

[0099] Figures 6-11 This is a schematic diagram illustrating the tracking effect of the present invention: In actual navigation, the path of the cooperative system includes curved segments. Figure 6 The 3D layout of the trajectories is shown. The initial states of the USV and UUV are set as follows: The virtual ship generates a parameterized reference path with switchable speeds. The time-varying disturbance applied to the controlled object is modeled as follows, assuming zero disturbance in the heave direction. This approach helps demonstrate the robustness of the proposed algorithm. The time-varying disturbances applied to the ship are shown below:

[0100] Figure 6 The trajectories of the actual ships (RS) under external disturbances are shown. It can be observed that the trajectories of both vehicles converge to the reference path with high accuracy. Furthermore, the proposed control algorithm guarantees high tracking accuracy. Figure 7 The position and attitude tracking errors of the two vehicles are presented. The results show that the UUV's errors are more stable and consistent compared to the USV. This performance difference can be attributed to the differences in the vehicles' mass and the external disturbances they experience. Overall, the proposed control method effectively ensures that both vehicles maintain all tracking errors within a small and acceptable range.

[0101] Figure 8-9 The actual control commands (propeller speed) generated for the aircraft based on the proposed algorithm are described. With rudder angle The clearly visible piecewise constant characteristics of these signals directly demonstrate the effective operation of the integral dynamic event triggering mechanism, which updates actuator instructions only when necessary, thereby significantly reducing communication load. Furthermore, these control inputs adhere to the actual saturation limits of the servo system and are constrained to... ( )and ( Within the range of ), it demonstrates the controller's inherent compliance with physical execution constraints.

[0102] Finally, the event trigger times and corresponding intervals are shown in Figure 10-11. A strict positive lower bound exists between consecutively triggered events, verifying that the proposed IDTM successfully eliminates the Zeno phenomenon and ensuring the practical feasibility of this control method.

[0103] 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 robust cooperative control method for surface-underwater vehicles considering communication limitations, characterized in that, include: S1: Establish kinematic and dynamic models for USV and UUV. The kinematic model is used to describe the relationship between the vehicle's velocity in the attached coordinate system and its attitude change rate in the geodetic coordinate system. The dynamic model is used to describe the relationship between the resultant force on the vehicle and its acceleration. S2: A master-slave collaborative architecture is adopted, defining the UUV as the first-level follower tracking the virtual ship and the USV as the second-level follower tracking the UUV; an atan2 function is introduced, and based on the kinematic model and the atan2 function, an improved adaptive LVS guidance law is designed. The improved adaptive LVS guidance law is used to compensate for the lateral drift caused by environmental disturbances online according to the position tracking error between the vehicle and the target and the introduced adaptive drift angle estimation term, so as to generate an improved guidance signal. S3: Based on the dynamic model, an adaptive segmented boundary compensation method is designed. The compensation method is used to softly divide the operating state space of the vehicle and use regression vectors of different complexities in each sub-region after division. The fusion output is generated by weighted fusion to approximate the unknown nonlinear dynamic terms in the system online. S4: Based on the guidance signal and the fusion output, a virtual control law and an actual control law are designed using the backstepping method. The virtual control law is used to calculate the desired speed based on the position error and heading angle error, and then define the speed error. The actual control law is used to calculate the desired control torque based on the speed tracking error and the fusion output. S5: Construct a nonlinear decay law and introduce an adaptive offset driven by the tracking error. Based on the dynamic gain controlled by the nonlinear decay law and the adaptive offset, a dynamic threshold is formed. Under communication-limited conditions, an improved integral dynamic event triggering mechanism is designed. The integral dynamic event triggering mechanism is used to determine the speed command and rudder angle command according to the dynamic threshold and decide whether to update the control command of the actuator. S6: Introduce actuator gain compensation coefficient, design actuator mapping and saturation processing to convert the desired control torque into propeller speed command and rudder angle command; after the event trigger judgment is passed, the command is physically limited to generate the final control command to realize master-slave cooperative path tracking control of virtual ship guiding UUV and UUV guiding USV.

2. The robust cooperative control method for surface-underwater vehicles considering communication limitations as described in claim 1, characterized in that, Establish kinematic and dynamic models for USVs and UUVs, including: S11. Construct the kinematic models of USV and UUV, with the following formulas: The pose of the USV in the geodetic coordinate system is: , Indicates location, The velocity vector in the attached coordinate system represents the heading angle. ,in For oscillation speed, For sway speed, The bow roll rate is ; the UUV's pose is . The velocity vector is ; They represent USV and UUV respectively; Let be a rotation matrix, and its expression is: S12. Construct the dynamic models of USV and UUV, with the following formulas: in, The inertia matrix includes the added mass. and These represent the Coriolis-centripetal force matrix and the damping matrix, respectively. Indicates a bounded environmental disturbance; The actual control law to be designed; The term without external force is reduced to a scalar function, and its formula is: in, , , It is a scalar function, i.e., a nonlinear dynamic term; The dynamic equations of USV and UUV in component form based on scalar functions are as follows: 。 3. The robust cooperative control method for surface-underwater vehicles considering communication limitations as described in claim 2, characterized in that, A master-slave collaborative architecture is adopted, defining a UUV as the first-level follower tracking virtual vessel and a USV as the second-level follower tracking the UUV. An atan2 function is introduced, and based on the kinematic model and the atan2 function, an improved adaptive LVS guidance law is designed. This improved adaptive LVS guidance law is used to compensate online for lateral drift caused by environmental disturbances based on the position tracking error between the vehicle and the target and the introduced adaptive drift angle estimation term, in order to generate an improved guidance signal, including: S21. Based on the master-slave collaborative architecture, calculate the position tracking error of the UUV relative to the virtual ship and the position tracking error of the USV relative to the UUV, using the following formulas: in, , Indicates the actual position coordinates of the USV; , Indicates the actual location coordinates of the UUV; This represents the position tracking error of the UUV relative to the virtual ship. This indicates the position tracking error of the USV relative to the UUV; The coordinates of the virtual ship's desired position; and These represent the straight-line distance from the UUV to the virtual ship and the straight-line distance from the USV to the UUV, respectively. S22. Based on the aforementioned position tracking error, an improved guidance signal is designed for each aircraft, and its formula is as follows: in, For improved guidance signals, for function, This is the adaptive drift angle estimation term; S23. Design the update law for the adaptive drift angle estimation term, the formula of which is: in, For adaptive gain; This represents the expected heading angle of the UUV tracked by the USV. This represents the expected heading angle of the virtual ship being tracked by the UUV; ; This refers to the heading angle tracking error.

4. The robust cooperative control method for surface-underwater vehicles considering communication limitations as described in claim 3, characterized in that, Based on the aforementioned dynamic model, an adaptive segmented boundary compensation method is designed. This method softly partitions the operational state space of the vehicle and uses regression vectors of different complexities within each partitioned sub-region. A weighted fusion method is then used to generate a fused output to approximate the unknown nonlinear dynamic terms in the system online. This includes: S31. Define the velocity norm vector of the aircraft. ,Will The space is divided into three centers The membership degree is calculated using the Gaussian kernel function, and the formula is as follows: in, It is a constant used to control the kernel width. Membership degree; Normalize the membership degrees to obtain normalized weights, the formula of which is: satisfy ; S32. Within each central region, construct a polynomial regression vector of increasing order, with the following formula: S33. The fusion output of the sway and pitch channels is constructed based on the polynomial regression vector and normalized weights, and the formulas are as follows: in, For the fusion output of the oscillating channel, For the fusion output of the bow rocker channel, and Let be the optimal parameter vector to be estimated; Design an online adaptive law for the sway and yaw channels to estimate the optimal parameter vector, the formula of which is: in, and The speed tracking error to be solved is... To design gain.

5. The robust cooperative control method for surface-underwater vehicles considering communication limitations as described in claim 4, characterized in that, Based on the guidance signal and the fused output, a virtual control law and an actual control law are designed using the backstepping method. The virtual control law is used to calculate the desired velocity based on the position error and heading angle error, and then defines the velocity error. The actual control law is used to calculate the desired control torque based on the velocity tracking error and the fused output, including: S41. Based on the kinematic model, derive the derivatives of the position tracking error and the heading angle tracking error. The formula is as follows: The virtual control law is designed to stabilize the tracking error, and its formula is as follows: in, and These are the virtual control laws for the sway channel and the yaw channel, respectively, and numerically they are the expected reference values ​​for the sway velocity and yaw angular velocity. For design parameters, This is a time-varying offset term; this term regularizes the error along the flight path to ensure... The heading angle tracking error satisfies the following constraints: S42. A first-order instruction filter is used to filter the virtual control law. The formula is as follows: in, It is a time constant. and The virtual control law after filtering; filter error and The following constraints must be met: in, The term is a known bounded perturbation. S43. Define the speed tracking error, and its formula is: Differentiating it, the formula is: in, and For the sway and yaw channels, the inertia coefficients are denoted as . S44. Based on the derivative of the speed tracking error and the fused output, the unknown nonlinear function in the dynamic model is compensated, and the actual control law is designed. The formula is as follows: in, To design gain, and These are the actual control laws for the sway channel and the yaw channel, respectively, which are numerically equivalent to the desired control torque.

6. The cooperative robust control method for surface-underwater vehicles considering communication limitations as described in claim 5, characterized in that, A nonlinear decay law is constructed, and an adaptive offset driven by tracking error is introduced. Based on the dynamic threshold jointly formed by the dynamic gain controlled by the nonlinear decay law and the adaptive offset, an improved integral dynamic event triggering mechanism is designed under communication-constrained conditions. This mechanism is used to determine whether to update the control commands of the actuator based on the dynamic threshold, including: S51. Construct a nonlinear decay law, the formula of which is: An adaptive offset driven by the tracking error is introduced, based on a dynamic threshold jointly formed by the dynamic gain controlled by the nonlinear decay law and the adaptive offset, the formula of which is: in, , For dynamic gain, and It is a nonlinear decay law. and For adaptive offset, For design parameters; S52. Define the generalized thrust-related variable as a piecewise constant signal, which at the trigger time... The update remains unchanged between two triggers, and its formula is: in, Represents the generalized thrust-related variables. Indicates the propeller speed command. This is the rudder angle command; S53. Based on the dynamic threshold jointly constituted by the dynamic gain controlled by the nonlinear attenuation law and the adaptive offset, an integral event triggering condition is designed under communication-limited conditions to determine the next triggering moment. The trigger condition is defined by the following formula: 。 7. The robust cooperative control method for surface-underwater vehicles considering communication limitations as described in claim 6, characterized in that, An actuator gain compensation coefficient is introduced, and actuator mapping and saturation processing are designed to convert the desired control torque into propeller speed command and rudder angle command. After the event trigger determination is passed, the command is physically limited to generate the final control command, including: S61. To compensate for uncertain actuator gain, an actuator gain compensation coefficient is introduced. and And design its adaptive law, the formula of which is: in, For design parameters; and Initial value; S62. Upon reaching the trigger moment, based on the actuator gain compensation coefficient, the actual control law is converted into propeller speed command and rudder angle command, with the following formula: S63. When the triggering condition of an integral event is met, the next triggering time is reached. ， The speed command for the current control cycle and rudder angle commands Updated to control commands of the actual actuator and and in The instruction remains unchanged; when the triggering condition is not met, the actuator maintains the instruction value executed at the previous triggering time. S64. Apply saturation constraints to the propeller speed command and rudder angle command to satisfy the following conditions: in, and These are the maximum permissible values ​​for propeller speed and rudder angle, respectively.

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