Integral event-triggered hovering control method for underwater vehicle
By introducing an integral event triggering mechanism into the hovering control of underwater vehicles, the problem of high computational resource consumption of the MPC method is solved, achieving stable hovering control and saving computational resources.
Patent Information
- Application Number
- CN202511583161.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-31
- Publication Date
- 2026-02-06
AI Technical Summary
In existing technologies, the MPC method for hovering control of underwater vehicles (AUVs) consumes a lot of computational resources, leading to frequent online optimization problems and affecting control efficiency.
An integral event triggering mechanism is adopted, which constructs the triggering condition by integrating the error between the predicted state and the actual state, thereby reducing the frequency of optimization operations and achieving stable hovering control by combining it with the MPC method.
Under the condition of satisfying state constraints and input constraints, the computational resource consumption of AUV hovering control is reduced, stable hovering control is achieved, and computational resources are saved.
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Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of underwater vehicle hovering control, in particular to an integral event-triggered hovering control method for underwater vehicles, and is applied to the field of ocean engineering. BACKGROUND
[0002] Hovering control is one of the core technologies of AUV control, especially when performing tasks such as fixed-point monitoring and silent stealth detection, the stability and precision of hovering are crucial. For AUV equipped with VBS, its hovering control faces multiple constraint challenges. The input of the variable buoyancy regulation system can only take three discrete values of constant rate water injection (+1), shutdown (0) and water discharge (-1), while being limited by the capacity constraint of the ballast tank and the state constraint of the vehicle. In addition, the dynamic characteristics of the system are complex, and the control process needs to achieve stable and accurate depth control while meeting the constraints. Under this background, MPC becomes the optimal solution. MPC can consider all constraints based on the prediction of the future state of AUV, optimize the control sequence, and ensure that the regulation system can still achieve efficient and stable hovering control under the limited control freedom.
[0003] However, the MPC scheme solves an online optimization problem in each control period to solve the optimal control action sequence based on the state space model and the current state of the target system. However, the online optimization problem will result in a high computational burden, which is one of the key obstacles to implementing MPC-based AUV hovering control. In practical applications, most optimization operations are actually unnecessary during the entire hovering process, for example, some consecutive operations almost produce the same control action. Therefore, it is beneficial to reduce such redundant optimization operations by using an event-triggered mechanism (ETM) control strategy, thereby ensuring that the number of optimization solutions is reduced without sacrificing control performance, saving computing resources.
[0004] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present application, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY
[0005] In view of the problem of large consumption of computing resources caused by the MPC method for hovering control of AUV, the present application provides an integral event-triggered hovering control method for underwater vehicles, which realizes stable hovering control while introducing an integral event-triggered mechanism to save computing resources.
[0006] Other characteristics and advantages of the present application will become apparent from the following detailed description, or will be learned by practice of the present application.
[0007] According to a first aspect of the present invention, an integral event-triggered hovering control method for an underwater vehicle is provided, the method comprising: Step 1: Define the coordinate system required for modeling, define the state variables and control inputs, and make reasonable assumptions and simplifications based on the characteristics of hovering maneuvers; Step 2: Based on Step 1, establish the dynamics and kinematic equations for the four-degree-of-freedom hovering in the vertical plane; Step 3: Define the nominal system for AUV hovering, design the MPC optimization problem and its cost function; Step 4: Introduce an integral event triggering mechanism and design specific integral event triggering conditions.
[0008] In some exemplary embodiments, the simplification based on reasonable assumptions about the characteristics of hovering maneuvers specifically includes: The AUV is allowed to drift horizontally. When hovering, the main thruster is not working, there is no longitudinal speed, and no rudder is used. Depth and pitch angle are used as parameters for underwater hovering control.
[0009] In some exemplary embodiments, the dynamics of the four-degree-of-freedom hovering in the vertical plane are specifically as follows: The dynamic equations of the AUV in the vertical plane become:
[0010]
[0011] in, , For AUV quality, The density of seawater, For AUV length, This is the amount by which the center of gravity of the AUV is shifted forward. This represents the downward shift of the AUV's center of gravity. , and respectively along , and around The velocity and angular velocity of the shaft, For AUV buoyancy, , and These are the initial imbalance, the vertical force generated by the injection and drainage of ballast tanks, and the wave disturbance force near the water surface. , , They are respectively by , and The resulting pitching moment, , and These are dimensionless hydrodynamic parameters. The starting position for integration is the bow of the vehicle. The end point of integration is the stern of the AUV. The ordinate of the center of buoyancy, The ordinate of the centroid The vertical position coordinates of the center of gravity The vertical position coordinates of the center of buoyancy. This is the crossflow drag coefficient.
[0012] In some exemplary embodiments, the kinematic equations in the vertical plane of the AUV become
[0013]
[0014] in, For velocity vectors, This is the pose vector.
[0015] In some exemplary embodiments, the optimization problem of the MPC and its cost function are specifically as follows: remember and The first Given the predicted state sequence and control input sequence at time t, then, The optimization problem at this point is as follows:
[0016] The cost function is defined as follows:
[0017] in , and This is the weight matrix. For prediction in the time domain. After solving the optimization problem, the optimal control sequence is expressed as follows: The corresponding optimal state control sequence is ,in .
[0018] In some exemplary embodiments, the introduction of an integral event triggering mechanism and the design of specific integral event triggering conditions are as follows: Assuming the event is triggered at time ; in the Each sampling time Real state sequences are obtained from real nonlinear systems and MPC optimization problems, respectively. and the predicted optimal state sequence Because there are unknown but bounded addable perturbations in the system, and They will not be completely identical; they will adopt... and The integral of the difference between them serves as the trigger condition for the next sampling and solution; the trigger condition for the integral event is designed as follows:
[0019]
[0020] in, This is a threshold for error accumulation. Once the accumulated error reaches this threshold, the next sampling is triggered. The P-norm represents the deviation between the actual and predicted states; from The cumulative value of the integral error reaches at time t. At that time, the smallest Recorded as .
[0021] In some exemplary implementations, an upper bound is also included. ,final Pick and The minimum of the two.
[0022] According to a second aspect of the present invention, a storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the underwater vehicle integral event-triggered hovering control method described in the first aspect above.
[0023] According to a third aspect of the present invention, a computer program product is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, it implements the underwater vehicle integral event-triggered hovering control method described in the first aspect above.
[0024] According to a fourth aspect of the present invention, an electronic device is provided, comprising: Processor; and Memory for storing the executable instructions of the processor; The processor is configured to implement the underwater vehicle integral event-triggered hovering control method described in the first aspect above by executing the executable instructions.
[0025] The underwater vehicle integral event-triggered hovering control method provided by the embodiments of the present invention, compared with the prior art, can reduce the consumption of computational resources during AUV hovering control, thereby achieving stable hovering control while satisfying the state constraints of the AUV and the mixed integer constraints of the VBS. It has the following beneficial effects: (1) For hovering control, a multi-constraint input-output system, a hovering control scheme based on MPC is proposed, which realizes stable hovering control under switch control under the condition of satisfying the constraints; (2) An event triggering mechanism was introduced and an integral event triggering condition was designed, thereby reducing the frequency of optimization and saving computational resources while ensuring the performance of MPC control.
[0026] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description
[0027] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.
[0028] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the inertial coordinate system {A} and the moving coordinate system {B}. Figure 3 A diagram showing a predicted hovering control scheme for an integral event-triggered mechanism model; Figure 4 A comparison of hovering depth and vertical velocity for MPC and NMPC with integral event triggering mechanisms; Figure 5 MPC and NMPC hovering bow ballast tank switch and water volume for an integral event triggering mechanism; Figure 6 MPC and NMPC hovering stern ballast tank switch and water volume for an integral event triggering mechanism; Figure 7 A comparison of hovering pitch angle and angular velocity for MPC and NMPC with integral event triggering mechanisms; Figure 8 To optimize the solution time of the MPC trigger interval and trigger time for an integral event triggering mechanism; Figure 9 The solution time is optimized for NMPC trigger interval and trigger time. Detailed Implementation
[0029] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
[0030] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.
[0031] To address the shortcomings and deficiencies of existing technologies, this example embodiment provides an integral-type event-triggered hovering control method for underwater vehicles (VBS). More specifically, it addresses the significant computational burden on the nonlinear mixed-integer programming (MIPC) optimization problem caused by the VBS's switch control being limited to three discrete action values. By introducing the integral of the error between the predicted and actual state sequences to construct event triggering conditions, the solution frequency of the optimization problem is reduced, saving computational resources. Simultaneously, leveraging MPC's ability to handle state and input constraints, precise hovering control under VBS switch inputs is achieved.
[0032] refer to Figure 1 As shown, the specific steps may include: Step 1: Define the coordinate system required for modeling, define the state variables and control inputs, and make reasonable assumptions and simplifications based on the characteristics of hovering maneuvers; Step 2: Based on Step 1, establish the dynamics and kinematic equations for the four-degree-of-freedom hovering in the vertical plane; Step 3: Define the nominal system for AUV hovering, design the MPC optimization problem and its cost function; Step 4: Introduce an integral event triggering mechanism and design specific integral event triggering conditions; Step 5: Analyze the upper and lower bounds of the triggering time of the designed triggering conditions and provide a proof; Step 6: Verify the performance of the designed controller through mathematical simulation.
[0033] The steps in this exemplary embodiment will now be described in more detail with reference to the accompanying drawings and embodiments.
[0034] In step S1, to study the hovering maneuver of the AUV, it is necessary to determine the position and attitude of the AUV. Two coordinate systems are used as shown in the appendix below. Figure 2 As shown, the inertial coordinate system {A} is used to describe the position and attitude of the AUV, and the motion coordinate system {B} is used to describe the velocity and angular velocity of the AUV.
[0035] The hovering model of an AUV can be described in matrix form. (1) in, For velocity vectors, For pose vector, It is a generalized force vector. External disturbances. For the inertia matrix, For the Coriolis centripetal force matrix, For the damping force matrix, This is the static matrix.
[0036] Since VBS can only control the net buoyancy change in the vertical plane of the AUV, horizontal position is not controlled, allowing horizontal drift. Furthermore, the main thrusters are not engaged during hovering, and there is no longitudinal speed or rudder operation. The main parameters for controlling underwater hovering are depth and pitch angle.
[0037] In step S2, under the above assumptions and definitions, the dynamic equations in the vertical plane of the AUV become: (2) (3) in, , For AUV quality, The density of seawater, For AUV length, This is the amount by which the center of gravity of the AUV is shifted forward. This represents the downward shift of the AUV's center of gravity. , and respectively along , and around The velocity and angular velocity of the shaft, For AUV buoyancy. , and These are the initial imbalance, the vertical force generated by the injection and drainage of ballast tanks, and the wave disturbance force near the water surface. , , They are respectively by , and The resulting pitching moment. , and These are dimensionless hydrodynamic parameters. The starting position for integration is the bow of the vehicle. The end point of integration is the stern of the AUV. The ordinate of the center of buoyancy, The ordinate of the centroid The vertical position coordinates of the center of gravity The vertical position coordinates of the center of buoyancy. This is the crossflow drag coefficient.
[0038] The kinematic equations of the AUV in the vertical plane become: (4) (5) In step S3, the continuous-time nonlinear system with additional disturbances in formula (1) can be written as follows: (6) in, , , These are the system state, control input, and an unknown, single-bounded external disturbance. The system satisfies... And has a Lipschitz constant. Disturbance Belongs to compact set Its upper limit is The nominal system of formula (6) is shown below. (7) This nominal system is used to construct the equality constraints for optimization problems. and The first The predicted state sequence and control input sequence at time step. Then, at... The optimization problem at this point is as follows: (8) The cost function is defined as follows: (9) in , and This is the weight matrix. For prediction in the time domain. After solving the optimization problem, the optimal control sequence is expressed as follows: The corresponding optimal state control sequence is ,in .
[0039] In step S4, to effectively reduce the number of optimization solutions, lower the computation frequency, and save computational resources, an integral event-triggered mechanism is introduced to achieve the above requirements while completing the control task. Assume the event trigger time is... In the first Each sampling time Real state sequences can be obtained from real nonlinear systems (6) and MPC optimization problems, respectively. and the predicted optimal state sequence Because the system contains unknown but bounded addable perturbations, and They will not be completely identical. Therefore, one can adopt... and The integral of the difference between the two values serves as the trigger condition for the next sampling and solution. Therefore, the trigger condition for the integral event is designed as follows: (10) (11) in, This is the threshold for error accumulation. Once the accumulated error reaches this threshold, the next sampling is triggered. The P-norm represents the deviation between the actual and predicted states. The cumulative value of the integral error reaches at time t. At that time, the smallest Recorded as . The physical meaning is expressed in After that, the system can run for a period of time. No resampling is required. Determines the next trigger time However, to avoid excessively long trigger times and ensure effective control, an upper limit was set. (Predicting the time domain), take the minimum of the two, that is... The event triggering conditions must be met, but the maximum allowable value in the prediction time domain must not be exceeded.
[0040] In step S5, for the nonlinear system in (6), the event triggering time is realized according to the above integral event triggering mechanism. , Then the following properties hold: 1) The upper bound of the time interval between two adjacent triggers is ; 2) The lower bound is Thresholds can be triggered through proper design To ensure, as shown below (12) in: It is a scale parameter.
[0041] Proof: This proof can be divided into two steps.
[0042] Step 1: The upper bound of the time interval between two adjacent triggers is From the design of the integral ETM, all intervals can be directly derived. All are less than or equal to the prediction time domain .
[0043] Step 2: Appropriately design the error accumulation trigger threshold through (13) The lower bound of the time interval between two adjacent triggers can be set as To prove this result, let's first consider... time The upper bound of the value. We assume the sensor measurement is accurate, therefore (13) By using the triangle inequality, we can obtain... (14) Then, applying the integral form of the Gronwall-Bellman inequality, we can obtain... (15) It can be deduced (16) Because when hour, Strictly greater than zero, we can choose the appropriate This makes the lower bound of the trigger time interval . The proof is complete.
[0044] In step S6, based on the aforementioned kinematic and dynamic model, and the model predictive control scheme based on the integral event triggering mechanism, as shown in the appendix... Figure 3 As shown, simulation software was built to perform mathematical simulation analysis.
[0045] The invention is further illustrated below through simulation experiments: Let the initial state of the AUV be... The target state is The task is for the AUV to freely submerge from an initial depth of 5m using the water inlet and outlet of the VBS, thereby reaching the desired hovering depth of 15m.
[0046] From simulation results Figure 4 , Figure 5 , Figure 6 and Figure 7 It can be seen that in the initial stage of the mission, due to the existence of depth error, both the bow and stern ballast tanks were filled with ballast water, causing the AUV to sink rapidly until the ballast water in the bow and stern tanks was emptied at 71 seconds to begin deceleration. At 105 seconds, the AUV reached the target hovering depth. During the hovering stabilization phase, the depth error was less than 0.25m, and the pitch oscillation was less than 1°. However, due to the oscillation of the pitch angle, the bow and stern ballast tank switches also performed water injection and drainage operations accordingly to control the pitch attitude and stabilize it within an acceptable range. Compared with the periodic NMPC, the IT ETM-MPC has slightly lower control accuracy. This is because IT ETM differs from traditional periodic control; it only achieves its accuracy when the state error accumulates to a threshold. Only when a new optimization solution is triggered does the system's dynamic response slow down, thus affecting control accuracy. Although this method sacrifices some control performance, it greatly reduces the computational burden.
[0047] Depend on Figure 8 and Figure 9 It can be seen that the optimization problem solving frequency of the integral ET-MPC is much lower than that of the NMPC, and in most cases, the trigger interval remains at the maximum value of 5 seconds, indicating that the controller does not frequently trigger optimization for most of the time. Furthermore, in this task, the integral ET-MPC took 32.125 seconds to solve the optimization problem, while the NMPC took 114.298 seconds, demonstrating that ET-ETM is effective in reducing computational burden.
[0048] In summary, the integral-type ETM-MPC proposed in this invention can save more communication resources by performing less frequent event-triggered sampling while ensuring control performance, which is more advantageous than the traditional NMPC.
[0049] It should be noted that, as another aspect, this application also provides a storage medium, which may be included in an electronic device or may exist independently without being assembled into the electronic device. The storage medium carries one or more programs, which, when executed by an electronic device, cause the electronic device to perform the methods described in the following embodiments.
[0050] In one embodiment, this application provides a computer program product including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.
[0051] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.
[0052] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.
[0053] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined only by the appended claims.
Claims
1. A hovering control method for an underwater vehicle based on an integral event triggering mechanism, characterized in that, The method includes: Step 1: Define the coordinate system required for modeling, define the state variables and control inputs, and make reasonable assumptions and simplifications based on the characteristics of hovering maneuvers; Step 2: Based on Step 1, establish the dynamics and kinematic equations for the four-degree-of-freedom hovering in the vertical plane; Step 3: Define the nominal system for AUV hovering, design the MPC optimization problem and its cost function; Step 4: Introduce an integral event triggering mechanism and design specific integral event triggering conditions.
2. The method according to claim 1, characterized in that, The simplification based on reasonable assumptions about the characteristics of hovering maneuvers is as follows: The AUV is allowed to drift horizontally. When hovering, the main thruster is not working, there is no longitudinal speed, and no rudder is used. Depth and pitch angle are used as parameters for underwater hovering control.
3. The method according to claim 2, characterized in that, The dynamics of the four-degree-of-freedom hovering in the vertical plane are as follows: The dynamic equations of the AUV in the vertical plane become: in, , For AUV quality, The density of seawater, For AUV length, This is the amount by which the center of gravity of the AUV is shifted forward. This represents the downward shift of the AUV's center of gravity. , and respectively along , and around The velocity and angular velocity of the shaft, For AUV buoyancy, , and These are the initial imbalance, the vertical force generated by the injection and drainage of ballast tanks, and the wave disturbance force near the water surface. , , They are respectively by , and The resulting pitching moment, , and These are dimensionless hydrodynamic parameters. The starting position for integration is the bow of the vehicle. The end point of integration is the stern of the AUV. The ordinate of the center of buoyancy, The ordinate of the centroid The vertical position coordinates of the center of gravity The vertical position coordinates of the center of buoyancy. This is the crossflow drag coefficient.
4. The method according to claim 3, characterized in that, The kinematic equations in the vertical plane of the AUV become: in, For velocity vectors, This is the pose vector.
5. The method according to claim 4, characterized in that, The optimization problem of MPC and its cost function are as follows: remember and The first Given the predicted state sequence and control input sequence at time t, then, The optimization problem at this point is as follows: The cost function is defined as follows: in , and This is the weight matrix. For prediction in the time domain. After solving the optimization problem, the optimal control sequence is expressed as follows: The corresponding optimal state control sequence is ,in .
6. The method according to claim 5, characterized in that, The introduction of an integral event triggering mechanism, and the design of specific integral event triggering conditions, are as follows: Assuming the event is triggered at time ; in the Each sampling time Real state sequences are obtained from real nonlinear systems and MPC optimization problems, respectively. and the predicted optimal state sequence Because there are unknown but bounded addable perturbations in the system, and They will not be completely identical; they will adopt... and The integral of the difference between them serves as the trigger condition for the next sampling and solution; The triggering conditions for integral events are designed as follows: in, This is a threshold for error accumulation. Once the accumulated error reaches this threshold, the next sampling is triggered. The P-norm represents the deviation between the actual and predicted states; from The cumulative value of the integral error reaches at time t. At that time, the smallest Recorded as .
7. The method according to claim 6, characterized in that, It also includes setting an upper limit. ,final Pick and The minimum of the two.
8. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the underwater vehicle integral event-triggered hovering control method as described in any one of claims 1 to 7.
9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the underwater vehicle integral event-triggered hovering control method as described in any one of claims 1 to 7.
10. An electronic device, characterized in that, include: processor; as well as Memory for storing the executable instructions of the processor; The processor is configured to execute the underwater vehicle integral event-triggered hovering control method according to any one of claims 1 to 7 by executing the executable instructions.