Event triggering type unmanned underwater vehicle model prediction control method

Abstract

The invention discloses an event-triggered unmanned underwater vehicle model prediction control method, which can effectively reduce the calculation cost while ensuring the trajectory tracking performance by executing the motion and path planning of a UUV (Unmanned Underwater Vehicle) at different frequencies. When a trajectory tracking error reaches a preset threshold value or the UUV approaches a target trajectory end point, the system triggers generation of a new reference trajectory, so that the adaptability of path tracking is improved. According to the event triggering MPC algorithm, kinematics and dynamics models of the UUV are combined, it is ensured that a controller can accurately track a feasible reference trajectory, and therefore the gap between motion planning and control is effectively bridged.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater vehicles, and in particular relates to an event-triggered unmanned underwater vehicle model predictive control method. Background Art

[0002] The underwater environment is extremely complex and harsh, with a wide variety of marine life and the challenges of natural conditions such as high pressure, low temperature, and strong currents. These factors pose enormous difficulties for deep-sea operations. To meet these challenges and efficiently carry out large-scale exploration and development of marine resources, while reducing the threat to personnel safety in high-risk environments, underwater unmanned vehicles (UUVs) have emerged. With their unique advantages, UUVs have become an indispensable tool in fields such as marine exploration, resource extraction, and scientific research. Compared with traditional underwater operation methods, UUVs exhibit many significant advantages: they do not require human operation, which greatly reduces the risks of deep-sea operations and avoids direct human contact with dangerous environments; they have a high degree of autonomy, can independently perform operations according to preset tasks, and can flexibly adjust strategies according to environmental changes during the execution of tasks. In addition, UUVs have extremely excellent control performance and can accurately complete complex tasks.

[0003] When evaluating UUV mission capabilities, motion control capabilities are a key criterion for determining their intelligence. With the continuous advancement of manufacturing and control technologies, modern small UUVs are now capable of performing missions in increasingly complex and demanding environments, placing even stricter demands on their mission capabilities. This is particularly true in areas such as deep-sea resource exploration and seabed topography analysis, where motion control capabilities face even greater challenges. MPC can adjust control inputs in real time based on the UUV's current state, enabling it to adapt to dynamically changing environments and uncertainties, while providing high path tracking accuracy.

[0004] The model predictive control (MPC) algorithm consists of three core components: model prediction, rolling optimization, and feedback correction. Within each rolling horizon, MPC utilizes the latest system state for optimization and solution to determine the current control input. Through online optimization, MPC can adjust the control strategy in real time based on the UUV's state, adapting to the dynamic environment and system uncertainty, and providing excellent path tracking accuracy. Furthermore, MPC has a natural advantage in handling input and output constraints, enabling it to effectively cope with complex constraints. This capability is particularly important for UUVs to perform missions in complex environments, ensuring their high efficiency and reliability in challenging scenarios.

[0005] To address the path tracking problem of multiple UUV formations, researchers have designed a new method that combines behavioral methods with line-of-sight guidance. This method can achieve precise tracking of the target path by UUVs while maintaining the predetermined formation shape. Cascade control theory can construct a dynamic model of path tracking errors, and the consistent semi-global exponential stability of the closed-loop system has been proven. An improved fast marching algorithm is used to quickly plan the two-dimensional continuous path of the UUV, and the turning radius is used as a constraint to optimize path selection. Based on the idea of ​​virtual potential field gradients, an improved numerical path planning method is designed. This method is easy to implement numerical packaging and is very suitable for application in UUV controllers.

[0006] Model predictive control (MPC), as an advanced feedback control strategy, has been widely used in engineering practice. For UUVs with vertical slot thrusters, the MPC method is used to adjust their depth and pitch angle in the hovering state, taking into account the constraints of the thrusters. Researchers designed a non-switching analytical MPC control method for uncertain nonlinear systems. This method keeps the control input unchanged during the sampling period, and based on this, the MPC is deduced, thereby expanding its application range. Combining MPC with exact feedback linearization technology, a control framework combining model predictive control and fuzzy logic control was designed. The input constraint problem is handled by a simple projection transformation, achieving good control effect. The robust MPC algorithm based on minimum and maximum values ​​ensures that the constraints can be met under all uncertainties, thereby improving the robustness of the control. In addition, the control method based on the robust one-step set constructs an extended terminal constraint set by expanding the initial state allowed region and using the offline designed polyhedron invariant set, and its effective suppression of bounded interference is demonstrated in simulation. The sensitivity-based nonlinear MPC algorithm combines a full-space interior-point nonlinear programming solution with nonlinear programming sensitivity analysis, splitting the optimization process into an offline calculation and a minimization online calculation, effectively avoiding computational delays. Numerous approaches are worth exploring to improve model predictive capabilities and efficiency, thereby optimizing path-tracking control.

[0007] However, traditional MPC algorithms plan and track reference trajectories at the same fixed frequency, which means that the receding horizon optimization problem needs to be solved at each time step, which is computationally intensive. Traditional MPC algorithms rely on a fixed sampling frequency, which can easily lead to insufficient response or excessive computational effort during actual UUV navigation. When rapid response is required, trajectory updates are slow, while in more stable motion states, the sampling frequency cannot be reduced, increasing the computational burden. In addition, the MPC algorithm's responsiveness is weak in the face of emergencies, resulting in large trajectory tracking errors. To address the computational complexity of optimization problems, it is necessary to explore more efficient optimization algorithms to accelerate the solution process and improve real-time adjustment capabilities. Summary of the Invention

[0008] To overcome the shortcomings of existing technologies, this paper provides an event-triggered model predictive control method for unmanned underwater vehicles. By executing the UUV's motion and path planning at different frequencies, this method effectively reduces computational costs while ensuring trajectory tracking performance. When the trajectory tracking error reaches a preset threshold or the UUV approaches the target trajectory endpoint, the system triggers the generation of a new reference trajectory, thereby improving the adaptability of path tracking. This event-triggered MPC algorithm combines the UUV's kinematic and dynamic models to ensure that the controller can accurately track a feasible reference trajectory, effectively bridging the gap between motion planning and control.

[0009] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0010] Step 1: Construct the planar kinematic model and dynamic model of the underactuated UUV;

[0011] Step 2: Path planning trigger rule formulation;

[0012] Step 3: UUV motion controller design;

[0013] Preferably, the step 1 is specifically:

[0014] Step 1-1: Establish a reference coordinate system to describe the UUV motion;

[0015] Underwater three-dimensional motion is represented by a rectangular coordinate system, including the earth coordinate system, i.e., the fixed coordinate system, and the hull coordinate system, i.e., the moving coordinate system.

[0016] The coordinate system is transformed to describe the mapping of the UUV's motion in the body coordinate system to the change in the earth coordinate system. The velocity transformation matrix is:

[0017]

[0018] Among them, η2 represents the attitude angle vector of UUV, ψ represents the heading angle, θ represents the pitch angle, and φ represents the roll angle;

[0019] The angular velocity transformation matrix is:

[0020]

[0021] Step 1-2: The kinematic and dynamic model expressions of UUV are as follows:

[0022]

[0023] Where M is the inertia matrix, C is the Coriolis centripetal force matrix, D is the damping matrix, g is the restoring torque, τ is the control force matrix generated by the actuator, η is the state vector of the UUV in the earth coordinate system, v is the state vector of the UUV in the hull coordinate system, and J(η) represents the transformation matrix, which is used to convert the hull velocity into the position and attitude change rate in the earth coordinate system;

[0024] Ignore the coupling effect between horizontal and vertical motions and remove the nonlinear quadratic damping term in the dynamic model;

[0025] The kinematic equation and dynamic equation of the underactuated UUV on the horizontal plane can be expressed as follows:

[0026]

[0027] and

[0028]

[0029] in:

[0030]

[0031] X represents forward thrust, N represents steering torque, v x represents the velocity along the x-axis in the body coordinate system, i.e., the forward velocity, v y represents the velocity along the y-axis in the body coordinate system, i.e., the lateral velocity; r represents the yaw angular velocity, i.e., the rotational angular velocity around the z-axis; m represents the mass of the UUV; and X represents the u' , Y v' , N r' They represent the additional mass coefficient in the acceleration direction; I zz represents the moment of inertia of UUV around the z axis, X u represents the linear damping coefficient in the forward direction, X uu represents the nonlinear damping coefficient in the forward direction, Y v Indicates the linear damping coefficient in the lateral direction, Y vv Indicates the nonlinear damping coefficient in the lateral direction, N r Indicates the linear damping coefficient in the yaw direction, N rr represents the nonlinear damping coefficient in the yaw direction;

[0032] The expression of the control input vector is:

[0033]

[0034] Preferably, the step 2 is specifically as follows:

[0035] Step 2-1: Design trigger rules to use the path tracking error. The optimization problem will only be executed when the error reaches the set threshold, i.e., the trigger level. The trigger time is defined as:

[0036]

[0037] Where Δ is the trigger level, P is the weighted matrix of the path tracking error, is the trigger moment, indicating that the trajectory tracking error reaches the trigger level; x pre (.) represents the state of the predicted trajectory at the prediction time s, x act (.) represents the state of the actual trajectory at the prediction time s, that is, the real system state, s represents the current continuous time variable, t k Indicates the last event triggering time, that is, the time of the kth control update; t k+1 Indicates the next event triggering moment, that is, the error between the system state and the predicted trajectory reaches the threshold;

[0038] Step 2-2: The trigger time is determined by the error between the reference trajectory and the actual trajectory, which is expressed as:

[0039]

[0040] Among them, A represents the state matrix of the system, B represents the control input matrix, d represents the disturbance term, which is a bounded disturbance function, τ pre represents the control input for the model predictive controller, x pre represents the predicted state optimized by the model predictive controller, x act Indicates the actual trajectory status of the UUV;

[0041] Step 2-3: Assume that the perturbation d is bounded and ρ is the upper bound; Assume that the maximum eigenvalue of matrix A is The largest eigenvalue of the matrix P is but:

[0042]

[0043] Using the Grownwall-Bellman inequality, we can get:

[0044]

[0045] The trigger level expression is:

[0046]

[0047] Where β is the trigger parameter, which determines the lower bound of the trigger period;

[0048] Step 2-4: Activate trajectory generation when the trajectory tracking error reaches the trigger level; define the prediction time length as T, and if the trigger rule is not met within the prediction range, the trigger time is t k +T; the total trigger condition expression is as follows:

[0049]

[0050] Among them, t k+1 is the final trigger time;

[0051] There are two trigger conditions: one is when the tracking error of the actual state trajectory to the optimal state trajectory reaches the threshold, which is the time The second is triggered when the UUV reaches the end of the previous predicted horizon, which is t k +T; According to the trigger level and trigger conditions, the time interval between two trigger points is defined as [βT, T]; if the trigger conditions are met, a new control task is calculated, otherwise the previous control task is used to control the UUV at each time step.

[0052] Preferably, the step 3 is specifically as follows:

[0053] Step 3-1: Considering the actuator capabilities of the UUV and the safety of the control system, embed state constraints and input constraints in the control algorithm to ensure the feasibility of the planned trajectory and enable the UUV to change its path along the planned trajectory;

[0054] The UUV constraints are:

[0055]

[0056] Among them, v xmin represents the minimum value of the velocity along the x-axis in the body coordinate system, v xmax represents the maximum velocity along the x-axis in the body coordinate system, v ymax Represents the maximum value of the velocity along the y-axis in the body coordinate system, r max Indicates the maximum value of the yaw angular velocity, y emin Indicates the minimum value of the UUV lateral error, y emax Indicates the maximum value of the UUV lateral error, X max Indicates the maximum forward thrust, N max Indicates the maximum value of the steering torque, y e (t) represents the lateral error, i.e., the error between the desired trajectory and the current position along the y direction;

[0057] The above formula can be rearranged into:

[0058]

[0059] Among them, τmin represents the lower bound of the control input, τ represents the control input vector, τ max represents the upper bound of the control input, x min represents the lower bound of the state vector, x represents the state vector, x max represents the upper bound of the state vector;

[0060] Step 3-2: Based on the UUV motion model and combined with the cost function f(t k ) and the constraints, we finally get the expression of the tracking strategy:

[0061]

[0062] satisfy:

[0063] x min <x<x max

[0064] τ min <τ<τ max

[0065] x(t k |t k )=x(t k ),τ(t k |t k )=τ(t k )

[0066] s∈[t k ,t k +T]

[0067] Where R is the control force weight matrix; I is the control input change weight matrix; Q is the state deviation weight matrix; T is the prediction time domain length;

[0068] The expression of the tracking strategy is solved to obtain the control quantity for planning the path within the prediction range, so that the UUV can track the expected path.

[0069] A computer program enables a computer to execute the above-mentioned model predictive control method.

[0070] An electronic device comprises: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device performs the above-mentioned model predictive control method.

[0071] A computer-readable storage medium stores a computer program, which implements the above-mentioned model predictive control method when executed by a processor.

[0072] A chip includes: a processor for calling and running a computer program from a memory, so that a device equipped with the chip executes the above-mentioned model predictive control method.

[0073] A computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the above-mentioned model predictive control method is implemented.

[0074] The beneficial effects of the present invention are as follows:

[0075] 1. In the model predictive control (MPC) algorithm, a highly adaptable control objective function was designed, combining the kinematic and dynamic characteristics of the UUV to optimize motion control. Furthermore, considering the actuator's capacity limitations, corresponding state constraints were set to ensure that the planned trajectory is feasible during actual execution. This design approach not only effectively ensures the stability of the UUV under different operating conditions, but also avoids the risk of actuator overload or exceeding performance limits, thereby improving the robustness and reliability of the entire system.

[0076] 2. By designing trigger rules, the reference path is recalculated only when specific events occur, allowing the UUV's motion planning and control to be updated at varying frequencies. This not only improves the UUV's adaptability to trajectory tracking errors but also enhances the system's accuracy and responsiveness. This approach reduces the computational burden by minimizing unnecessary path updates and precisely adjusts the control strategy when events occur, ensuring the UUV can complete trajectory tracking tasks more flexibly and accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 Schematic diagram of UUV underwater movement;

[0078] Figure 2 Schematic diagram of UUV control under MPC;

[0079] Figure 3 Design algorithm flow chart for UUV motion controller;

[0080] Figure 4 Schematic diagram of tracking trajectory under event-triggered MPC;

[0081] Figure 5 Schematic diagram of UUV motion tracking error;

[0082] Figure 6 Schematic diagram of the motion trajectory of UUV under traditional MPC. DETAILED DESCRIPTION

[0083] The present invention will be further described below with reference to the accompanying drawings and examples.

[0084] This paper proposes an event-triggered model predictive control (MPC) approach. By executing the UUV's motion and path planning at different frequencies, this approach effectively reduces computational costs while maintaining trajectory tracking performance. When the trajectory tracking error reaches a preset threshold or the UUV approaches the target trajectory endpoint, the system triggers the generation of a new reference trajectory, thereby improving the adaptability of path tracking. This event-triggered MPC algorithm incorporates the UUV's kinematic and dynamic models to ensure that the controller accurately tracks a feasible reference trajectory, effectively bridging the gap between motion planning and control.

[0085] 1. Planar kinematic and dynamic models of underactuated UUV;

[0086] The construction of the UUV model involves both kinematic and dynamic modeling. The kinematic model primarily studies the UUV's motion mapping between different coordinate systems, describing its motion in the moving coordinate system and its position changes in the Earth coordinate system, and analyzing the relationship between the UUV's velocity and displacement in the fixed coordinate system. The dynamic model analyzes the external forces and torques acting on the UUV, establishes the relationship between generalized forces and generalized accelerations, and studies the impact of these forces and torques on the UUV's acceleration.

[0087] like Figure 1 As shown in the figure, in order to study the motion law of UUV underwater and analyze its position information, it is necessary to first establish a reference coordinate system to describe the UUV motion. Usually, underwater three-dimensional motion is represented by a rectangular coordinate system, including the earth coordinate system (fixed coordinate system) and the hull coordinate system (moving coordinate system):

[0088] In order to describe the mapping of the UUV's motion in the body coordinate system to the change in the earth coordinate system, the coordinate system needs to be transformed. The velocity transformation matrix is:

[0089]

[0090] The angular velocity transformation matrix is:

[0091]

[0092] The kinematic and dynamic model expressions of UUV are as follows:

[0093]

[0094] In the underactuated UUV dynamic model, M is the inertia matrix, C is the Coriolis centripetal force matrix, D is the damping matrix, g is the restoring torque, τ is the control force matrix generated by the actuator, η is the UUV state vector in the earth coordinate system, and v is the UUV state vector in the hull coordinate system. To simplify the model, the coupling effects between horizontal and vertical motion are ignored, and the nonlinear quadratic damping term in the dynamic model is removed.

[0095] The kinematic equation and dynamic equation of the underactuated UUV on the horizontal plane can be expressed as follows:

[0096]

[0097] and

[0098]

[0099] in:

[0100]

[0101] The expression of the control input vector is:

[0102]

[0103] Where X represents the forward thrust and N represents the steering torque.

[0104] 2. Path planning trigger rule formulation;

[0105] The traditional model predictive controller predicts the system output in the future time domain by using the current UUV state measurement value and the prediction model. By solving the optimization problem that satisfies the objective function and various constraints, a series of control variable sequences in the time domain are obtained. The first element in the control sequence is used as the actual control quantity of the controlled object. When it comes to the next time k+1, the above process is repeated to achieve continuous control of the UUV. Its basic principle diagram is shown in the figure below. Figure 2 ;

[0106] Traditional MPC typically requires an online optimization solution for each control cycle, which places high demands on computing and communication resources. A key feature of event-triggered MPC is that control updates aren't performed at fixed intervals. Instead, the decision to update the control strategy is made dynamically based on certain triggering conditions or events (such as system state errors or changes in control inputs). This allows the system to maintain good control performance without requiring frequent calculations, significantly reducing the computational and communication burdens.

[0107] The present invention establishes triggering rules to determine when to activate a new trajectory planning strategy. When the trigger condition is met, the corresponding control forces are calculated within the predicted range. At the next trigger point, the event-triggered MPC algorithm repeats this process until the UUV reaches the target trajectory. This reduces the computational burden by allowing the trajectory to be planned only when the trigger condition is met. Control tasks are calculated and applied at each time step to track the planned trajectory. Motion planning and control of the UUV are executed at different frequencies.

[0108] The present invention takes into account external interference and modeling errors, which may cause the UUV to not accurately track the planned trajectory. There is inevitably a trajectory tracking error between the actual path and the planned path. Therefore, a trigger rule is designed to exploit the path tracking error. The optimization problem is only executed when the error reaches a set threshold (trigger level). The trigger time is defined as:

[0109]

[0110] Where Δ is the trigger level, P is the weighted matrix of the path tracking error, is the trigger moment, indicating that the trajectory tracking error reaches the trigger level. If the trigger level is set too low, it will lead to frequent replanning of the desired trajectory obtained by the optimization problem; while if the trigger level is set too high, the trajectory tracking error will be amplified. Therefore, it is necessary to select an appropriate trigger level. The trigger time is determined by the error between the reference trajectory and the actual trajectory, expressed as:

[0111]

[0112] The disturbance d causes the planned trajectory to be inconsistent with the actual trajectory. Assume that the disturbance is bounded and ρ is the upper bound. Let the maximum eigenvalue of matrix A be The largest eigenvalue of the matrix P is but:

[0113]

[0114] Using the Grownwall-Bellman inequality, we can get:

[0115]

[0116] The trigger level expression is:

[0117]

[0118] Where β is the trigger parameter, which determines the lower bound of the trigger period. The MPC algorithm is not triggered at a fixed time period, but is executed only when the trigger level is reached. Therefore, the trajectory tracking error can be kept within the specified range.

[0119] The trajectory generation is activated when the trajectory tracking error reaches the trigger level. In addition, when the UUV reaches the end point of the planned trajectory, the UUV motion planning is also required. The prediction time length is defined as T. If the trigger rule is not satisfied within the prediction range, the trigger time is t k +T. The overall trigger condition expression is as follows:

[0120]

[0121] t k+1 is the final trigger time. There are two trigger conditions: one is when the tracking error of the actual state trajectory to the optimal state trajectory reaches the threshold, which is the time The second is triggered when the UUV reaches the end of the previous predicted horizon, which is t k +T. According to the trigger level and trigger conditions, the time interval between two trigger points is defined as [βT, T]. If the trigger conditions are met, a new control task is calculated, otherwise the previous control task is used to control the UUV at each time step.

[0122] 3. UUV motion controller design;

[0123] Considering the actuator capability of UUV and the safety of control system, state constraints and input constraints are embedded in the control algorithm to ensure the feasibility of the planned trajectory and enable UUV to change the path along the planned trajectory. The algorithm flow chart is as follows Figure 3 ;

[0124] The UUV constraints are:

[0125]

[0126] The above constraints can be used to ensure the feasibility of the planned trajectory. The above constraints can be organized as follows:

[0127]

[0128] The goal of the UUV motion control strategy is to find a tracking path that can quickly reach the target trajectory and calculate the control quantity within the predicted field of view. The definition of the cost function must consider both control cost and drive stability. Based on the UUV motion model and combining the cost function with the constraints, the tracking strategy expression is finally obtained:

[0129]

[0130] satisfy:

[0131] x min <x<x max

[0132] τmin <τ<τ max

[0133] x(t k |t k )=x(t k ),τ(t k |t k )=τ(t k )

[0134] s∈[t k ,t k +T]

[0135] Where R is the control force weight matrix; M is the control input change weight matrix; Q is the state deviation weight matrix; and T is the prediction time domain length. By solving the above optimization problem, the control variables for planning the path within the prediction range are obtained, achieving the goal of the UUV tracking the expected path.

[0136] Example:

[0137] To evaluate the performance of the event-triggered MPC algorithm, relevant parameters were set through simulation, and corresponding tracking trajectories were obtained. The tracking results were compared with those of the traditional MPC algorithm. The results show that the strategy significantly improves adaptability and response speed, thus achieving good results in UUV path tracking.

[0138] In the simulation, an event-triggered MPC algorithm is used to generate the planned trajectory and the actual tracking path. A reference trajectory is generated at the initial moment, and the UUV is driven to begin navigation. When the tracking error exceeds a threshold, a new reference trajectory is generated. Furthermore, when the UUV reaches the end of the planned trajectory, motion planning is repeated. At each time step, the corresponding control force is applied to obtain the actual tracking trajectory.

[0139] like Figure 4 As shown in the figure, the algorithm generates a total of four planning paths. The first reference trajectory is based on the initial position of the UUV, with the purpose of starting the navigation of the UUV. Through the calculated control force, the UUV tracks the planned trajectory. Due to the inevitable generation of trajectory tracking error, when the tracking error reaches the trigger threshold, a new MPC optimization algorithm is started. When the UUV navigates to the longitudinal position of 25m, 37m and 78m, the trajectory tracking error reaches the preset threshold, resulting in the abandonment of the previous planned trajectory and related control instructions, and the recalculation of the new trajectory and control strategy from the current position. By adopting the new control method, the UUV can travel along the new trajectory with a smaller error and finally move smoothly along the target trajectory. Figure 5 The tracking error throughout the process is shown, highlighting the effectiveness of the system in maintaining tracking performance;

[0140] from Figure 5 As can be seen in the figure, the path tracking error remains consistently within 0.2 meters. During the tracking process, as the error gradually increases and reaches a trigger condition, the path is replanned and a new trajectory is activated. Each time the trigger condition is met, the optimization algorithm regenerates the trajectory, ensuring that the tracking error remains within an acceptable range. This dynamic adjustment enables the UUV to effectively adapt to changing environmental conditions and ensures that its movements remain consistent with the intended trajectory. As a result, tracking performance is significantly improved throughout the entire process.

[0141] In addition, in the traditional MPC scheme, the reference trajectory and control sequence are periodically calculated at a fixed frequency at each time step. The actual navigation trajectory of the UUV is different from the planned trajectory. Figure 6

[0142] like Figure 6 As shown, the UUV's motion planning utilizes a fixed-frequency model predictive control approach. At each time step, the algorithm computes a planned path and a series of control sequences to guide the UUV along the target course. The primary control task is initially to drive the UUV to begin navigation. Subsequently, at each time step, a new reference trajectory is generated based on the fixed-frequency model predictive control strategy. This iterative process continues until the UUV successfully reaches the target path.

[0143] The UUV motion control strategy proposed in this paper significantly reduces the computational complexity while maintaining planning performance, enhances the adaptability of trajectory tracking, and effectively bridges the gap between UUV motion planning and control.

Claims

1. An event-triggered unmanned underwater vehicle model predictive control method, characterized in that: The steps include: Step 1: Construct the planar kinematic model and dynamic model of the underactuated UUV; Step 2: Path planning trigger rule formulation; Step 3: UUV Motion Controller Design.

2. The event-triggered model predictive control method for an unmanned underwater vehicle according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1-1: Establish a reference coordinate system to describe the UUV motion; Underwater three-dimensional motion is represented by a rectangular coordinate system, including the earth coordinate system, i.e., the fixed coordinate system, and the hull coordinate system, i.e., the moving coordinate system. The coordinate system is transformed to describe the mapping of the UUV's motion in the body coordinate system to the change in the earth coordinate system. The velocity transformation matrix is: Among them, η2 represents the attitude angle vector of UUV, ψ represents the heading angle, θ represents the pitch angle, and φ represents the roll angle; The angular velocity transformation matrix is: Step 1-2: The kinematic and dynamic model expressions of UUV are as follows: Where M is the inertia matrix, C is the Coriolis centripetal force matrix, D is the damping matrix, g is the restoring torque, τ is the control force matrix generated by the actuator, η is the state vector of the UUV in the earth coordinate system, v is the state vector of the UUV in the hull coordinate system, and J(η) represents the transformation matrix, which is used to convert the hull velocity into the position and attitude change rate in the earth coordinate system; Ignore the coupling effect between horizontal and vertical motions and remove the nonlinear quadratic damping term in the dynamic model; The kinematic equation and dynamic equation of the underactuated UUV on the horizontal plane can be expressed as follows: and in: X represents forward thrust, N represents steering torque, v x represents the velocity along the x-axis in the body coordinate system, i.e., the forward velocity, v y represents the velocity along the y-axis in the body coordinate system, i.e., the lateral velocity; r represents the yaw angular velocity, i.e., the rotational angular velocity around the z-axis; m represents the mass of the UUV; and X represents the u' , Y v' , N r' They represent the additional mass coefficient in the acceleration direction; I zz represents the moment of inertia of UUV around the z axis, X u represents the linear damping coefficient in the forward direction, X uu represents the nonlinear damping coefficient in the forward direction, Y v Indicates the linear damping coefficient in the lateral direction, Y vv Indicates the nonlinear damping coefficient in the lateral direction, N r Indicates the linear damping coefficient in the yaw direction, N rr represents the nonlinear damping coefficient in the yaw direction; The expression of the control input vector is:

3. The event-triggered model predictive control method for an unmanned underwater vehicle according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2-1: Design trigger rules to use the path tracking error. The optimization problem will only be executed when the error reaches the set threshold, i.e., the trigger level. The trigger time is defined as: Where Δ is the trigger level, P is the weighted matrix of the path tracking error, is the trigger moment, indicating that the trajectory tracking error reaches the trigger level; x pre (.) represents the state of the predicted trajectory at the prediction time s, x act (.) represents the state of the actual trajectory at the prediction time s, that is, the real system state, s represents the current continuous time variable, t k Indicates the last event triggering time, that is, the time of the kth control update; t k+1 Indicates the next event triggering moment, that is, the error between the system state and the predicted trajectory reaches the threshold; Step 2-2: The trigger time is determined by the error between the reference trajectory and the actual trajectory, which is expressed as: Among them, A represents the state matrix of the system, B represents the control input matrix, d represents the disturbance term, which is a bounded disturbance function, τ pre represents the control input for the model predictive controller, x pre represents the predicted state optimized by the model predictive controller, x act Indicates the actual trajectory status of the UUV; Step 2-3: Assume that the perturbation d is bounded and ρ is the upper bound; Assume that the maximum eigenvalue of matrix A is The largest eigenvalue of the matrix P is but: Using the Grownwall-Bellman inequality, we can get: The trigger level expression is: Where β is the trigger parameter, which determines the lower bound of the trigger period; Step 2-4: Activate trajectory generation when the trajectory tracking error reaches the trigger level; define the prediction time length as T, and if the trigger rule is not met within the prediction range, the trigger time is t k +T; the total trigger condition expression is as follows: Among them, t k+1 is the final trigger time; There are two trigger conditions: one is when the tracking error of the actual state trajectory to the optimal state trajectory reaches the threshold, which is the time The second is triggered when the UUV reaches the end of the previous predicted horizon, which is t k +T; According to the trigger level and trigger conditions, the time interval between two trigger points is defined as [βT, T]; if the trigger conditions are met, a new control task is calculated, otherwise the previous control task is used to control the UUV at each time step.

4. The event-triggered model predictive control method for an unmanned underwater vehicle according to claim 3, characterized in that: The step 3 is specifically as follows: Step 3-1: Considering the actuator capabilities of the UUV and the safety of the control system, embed state constraints and input constraints in the control algorithm to ensure the feasibility of the planned trajectory and enable the UUV to change its path along the planned trajectory; The UUV constraints are: Among them, v xmin represents the minimum value of the velocity along the x-axis in the body coordinate system, v xmax represents the maximum velocity along the x-axis in the body coordinate system, v ymax Represents the maximum value of the velocity along the y-axis in the body coordinate system, r max Indicates the maximum value of the yaw angular velocity, y emin Indicates the minimum value of the UUV lateral error, y emax Indicates the maximum value of the UUV lateral error, X max Indicates the maximum forward thrust, N max Indicates the maximum value of the steering torque, y e (t) represents the lateral error, i.e., the error between the desired trajectory and the current position along the y direction; The above formula can be rearranged into: Among them, τ min represents the lower bound of the control input, τ represents the control input vector, τ max represents the upper bound of the control input, x min represents the lower bound of the state vector, x represents the state vector, x max represents the upper bound of the state vector; Step 3-2: Based on the UUV motion model and combined with the cost function f(t k ) and the constraints, we finally get the expression of the tracking strategy: satisfy: x min <x<x max t min <t<t max x(t k |t k )=x(t k ),τ(t k |t k )=τ(t k ) s∈[t k ,t k +T] Where R is the control force weight matrix; I is the control input change weight matrix; Q is the state deviation weight matrix; T is the prediction time domain length; The expression of the tracking strategy is solved to obtain the control quantity for planning the path within the prediction range, so that the UUV can track the expected path.

5. A computer program, characterized in that The computer program enables a computer to execute the method according to any one of claims 1 to 4.

6. An electronic device, characterized in that: include: processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the method according to any one of claims 1 and 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

8. A chip, characterized in that: include: A processor, configured to call and run a computer program from a memory, so that a device equipped with the chip executes the method according to any one of claims 1 to 4.

9. A computer program product, characterized in that The computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the method according to any one of claims 1 to 4 is implemented.

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