Cross-medium aircraft control method based on adaptive LSTM and Tube MPC

Abstract

The invention discloses a cross-medium aircraft control method based on adaptive LSTM and Tube MPC, and belongs to the technical field of aircraft cross-medium navigation control. The problem that an existing vehicle is poor in self-adaptability and robustness during cross-medium navigation is solved. The method comprises the following steps: acquiring a cross-medium dynamic model of the aircraft by combining a Newton-Euler equation on the basis of stress and moment of force of the aircraft in a cross-medium process; acquiring a real-time attitude of the aircraft based on a height sensor and an attitude sensor; obtaining an immersion degree sequence of the aircraft by using the real-time attitude, inputting the immersion degree sequence into a pre-trained adaptive LSTM fluid parameter predictor, and obtaining time-varying fluid parameters; the time-varying fluid parameters are substituted into the aircraft cross-media dynamic model, and an updated aircraft cross-media dynamic model is obtained; and in combination with a Tube MPC robust controller, solving a control instruction at the current moment by using the real-time attitude and the expected attitude of the aircraft. The method is suitable for cross-medium aircraft control.

Description

Technical Field

[0001] This invention belongs to the field of cross-medium navigation control technology for aircraft. Background Technology

[0002] In recent years, with the continuous expansion of application scenarios for aircraft, their operating environments have extended from traditional structured fields to complex and ever-changing multi-media spaces encompassing water, land, and air. In key areas such as disaster relief, environmental monitoring, national defense, and resource exploration, the demand for amphibious vehicles with cross-domain maneuverability is becoming increasingly urgent. These vehicles, through innovative mechanical designs such as biomimetic structures, variable stiffness limbs, and hybrid propulsion systems, achieve dynamic transitions between different physical media, demonstrating excellent environmental adaptability.

[0003] However, the dynamic environment of cross-medium vehicles is highly heterogeneous and nonlinear, especially during the transient process of crossing the water-air interface, where the dynamic model undergoes drastic changes, accompanied by significant parameter uncertainties and unmodeled dynamics, such as fluid-rigid body coupling effects, wave-making drag, and cavitation. This "model mismatch" problem constitutes the core challenge in achieving high-precision and high-stability attitude control.

[0004] Currently, control strategies for cross-medium vehicles are mainly divided into two paradigms: "integrated control" and "unified control." Integrated control relies on the switching of multiple controllers. Although it can be optimized for specific media, it suffers from problems such as switching hysteresis, complex logic, and system redundancy. Unified control, especially model predictive control (MPC), avoids switching problems by constructing a full-condition optimization framework. However, its predictive performance is highly dependent on the accuracy of the model, making it difficult to capture the strongly nonlinear dynamic nature of cross-medium processes, and its robustness to unmodeled dynamics and strong external disturbances is limited. In addition, traditional PID control lacks foresight, and sliding mode control (SMC) suffers from chattering problems, making it difficult to independently handle cross-medium attitude control tasks. Summary of the Invention

[0005] This invention aims to address the problems of poor adaptability and robustness of existing vehicles during cross-medium navigation. It provides a cross-medium vehicle control method based on adaptive LSTM and Tube MPC.

[0006] The present invention discloses a cross-medium vehicle control method based on adaptive LSTM and Tube MPC, comprising:

[0007] Step 1: Based on the forces and moments acting on the vehicle during the cross-medium process, and in conjunction with the Newton-Euler equations, obtain the cross-medium dynamics model of the vehicle.

[0008] The forces and torques experienced by the aircraft during the cross-medium process include at least the additional mass force and torque, restoring force and torque, fluid resistance and torque, control force and torque, and Coriolis force and torque;

[0009] Step 2: Based on the altitude sensor and attitude sensor, obtain the real-time attitude of the vehicle, and use the real-time attitude of the vehicle to calculate the sequence of the vehicle's immersion degree;

[0010] A pre-trained adaptive LSTM fluid parameter predictor is used, with the sequence of vehicle submersion as input, to obtain time-varying fluid parameters;

[0011] Step 3: Input the time-varying fluid parameters into the transmedium dynamics model of the vehicle to obtain the updated transmedium dynamics model of the vehicle;

[0012] Step 4: Based on the updated dynamic model and the Tube MPC robust controller, the control command at the current moment is obtained by using the real-time attitude and desired attitude of the vehicle.

[0013] The Tube MPC robust controller is configured as: the same nominal model and auxiliary state feedback controller as the updated dynamics model;

[0014] The nominal model is subjected to constraints that have been compressed based on the minimum robust positive invariant set. The desired attitude is then used to solve the finite-time optimal control problem to obtain the nominal control quantity.

[0015] The auxiliary state feedback controller calculates the deviation between the real-time attitude and the nominal attitude at the corresponding time, restricts the deviation to an invariant compact set, and obtains the auxiliary feedback quantity; the nominal attitude is the attitude of the nominal model.

[0016] The nominal control quantity and the auxiliary feedback quantity together constitute the final control command.

[0017] Furthermore, in this invention, in step one, the transmedium dynamics model of the vehicle is as follows:

[0018]

[0019] in, and For the mass and inertia of the aircraft itself, Indicates added mass. Indicates the additional inertia. Indicates resilience, Indicates restoring torque. This indicates the resistance experienced by the aircraft. Indicates the resistance torque. Indicates control. Indicates control torque. and This represents the force and torque exerted by the Coriolis force on the aircraft; and These represent the linear velocity derivative and angular velocity derivative in the object coordinate system fixed to the vehicle, respectively.

[0020] Furthermore, in this invention, the restoring force for:

[0021]

[0022]

[0023] in, and These represent the forces of gravity and buoyancy acting on the spacecraft, respectively. This represents the rotation matrix that transforms the vehicle from the object coordinate system to the inertial coordinate system.

[0024] In the object's coordinate system, the lever arm of gravity is 0, so only buoyancy needs to be considered. The torque generated by the action;

[0025] This is the restoring torque. :

[0026]

[0027] in, It is the buoyancy lever arm.

[0028] Furthermore, in this invention, the resistance experienced by the aircraft... and resistance torque for:

[0029]

[0030] in, Indicates the drag loss coefficient. This represents the drag torque loss coefficient. This represents the drag force experienced by the aircraft in the X-axis direction. This represents the drag force experienced by the aircraft in the Y-axis direction. This represents the drag force experienced by the aircraft in the Z-axis direction. Indicates the impact on the aircraft The torque of the axial resistance. Indicates the impact on the aircraft The torque of the axial resistance. Indicates the impact on the aircraft The torque of the resistance in the axial direction.

[0031] Furthermore, in this invention, the force and torque exerted by the Coriolis force on the aircraft and Represented as:

[0032]

[0033] in, and For the mass and inertia of the aircraft itself, Represents the angular velocity in degrees within a coordinate system fixed to the aircraft. This represents the linear velocity of an object in a coordinate system fixed to the vehicle.

[0034] Furthermore, in this invention, the control force and control torque They are respectively:

[0035]

[0036] in, Indicates four propellers in The total thrust generated in the direction, These represent the four propellers orbiting each other. The torque of the shaft; specifically expressed as:

[0037]

[0038] In the formula, Indicates the arm length of the aircraft. yes and The ratio, and These are the propeller's thrust coefficient and power coefficient, respectively. , , and These represent the thrust of the four propellers.

[0039] Furthermore, in this invention, the method for calculating the sequence of the vehicle's immersion degree using the vehicle's real-time attitude in step two is as follows:

[0040] The altitude of the vehicle's center of gravity relative to the water surface is obtained in real time using altitude and attitude sensors. Euler angles of the aircraft Then calculate the immersion degree at time t. ;

[0041]

[0042] in, This indicates the height of the vehicle's center of mass relative to the water surface. Indicates the pitch angle of the aircraft. H represents the roll angle of the aircraft, and H represents the altitude of the aircraft. This represents the yaw angle of the aircraft, and the sequence of the aircraft's immersion degrees at each discrete time step t. for:

[0043]

[0044] in, The sequence length;

[0045]

[0046] Where N represents the total number of discrete time steps.

[0047] Furthermore, in this invention, in step three, the time-varying fluid parameters are:

[0048]

[0049] in, Represents the target fluid parameter vector. , , These represent the mass loss coefficients of the aircraft in the x, y, and z directions, respectively. These respectively indicate that the aircraft is in The coefficient of rotational inertia loss in the direction of rotation. They represent the aircraft. Drag loss coefficient in the direction, These respectively indicate that the aircraft is in The coefficient of resistance torque loss on the rotating shaft.

[0050] Furthermore, in this invention, in step three, the finite-time optimal control problem is expressed as:

[0051]

[0052] in, It controls the rate of change (increment) of the input. Indicates in Time Prediction The nominal state vector at time 1. This indicates predicting the control input at time k+i at time k. This indicates predicting the control input at time k+i-1 at time k. This represents the weighted Euclidean norm square. These are the prediction time domains, satisfying... , Represents the spatial domain of the prediction. These are the state tracking error weight matrix and the control input rate of change weight matrix, respectively. This is the terminal state weight matrix; This indicates the prediction at time k. The nominal state vector at time 1. This indicates the prediction at time k. The nominal state vector at time 1. Represents the expected value at time k. The reference state vector at time t.

[0053] Furthermore, in this invention, the constraints after compression based on the minimum robust positive invariant set are:

[0054]

[0055] in, , , Represents an invariant compact set, the actual system state Compared with nominal condition Deviation between , The discretized dynamic equations representing LSTM enhancement This represents the predicted value of the actual system state at time k+1 based on the value at time k. This represents the external disturbance term at time k+i. This represents the state constraint after compression. This represents the compressed input constraints. This represents the tightened input rate of change constraint. This indicates the rate of change of the control input.

[0056] This invention effectively compensates for the limitations of a single mechanistic model in describing cross-medium nonlinear dynamics by constructing a hybrid predictor that integrates a mechanistic model and a data-driven model. It employs an LSTM network to predict time-varying fluid parameters in real time, significantly improving the model's adaptive compensation capability for complex hydrodynamic effects during medium transitions. The introduction of the Tube-MPC framework explicitly handles model uncertainties and external disturbances, enhancing system robustness and control accuracy while ensuring constraint satisfaction. Simulation results demonstrate that the proposed LSTM-MPC controller outperforms traditional control methods in attitude angle tracking, position error suppression, and disturbance rejection, especially exhibiting superior performance during the water-air interface transition phase. Attached Figure Description

[0057] Figure 1This is a flowchart of the method described in this invention;

[0058] Figure 2 This is a framework diagram of the cross-medium vehicle control algorithm based on adaptive LSTM and Tube MPC of the present invention;

[0059] Figure 3 Diagram of an adaptive neural network structure;

[0060] Figure 4 This is a graph showing the absolute error between the test results and the true values ​​of the drag loss coefficient of the LSTM neural network in the xyz direction according to the present invention.

[0061] In the figure, (a) represents the absolute error curve between the test results and the true value of the drag loss coefficient in the x direction, (b) represents the absolute error curve between the test results and the true value of the drag loss coefficient in the y direction, and (c) represents the absolute error curve between the test results and the true value of the drag loss coefficient in the z direction.

[0062] Figure 5 This is a graph showing the absolute error between the test results and the true values ​​of the LSTM neural network drag torque loss coefficient in the xyz direction.

[0063] In the figure, (a) represents the absolute error curve between the test result and the true value of the drag torque loss coefficient in the x direction, (b) represents the absolute error curve between the test result and the true value of the drag torque loss coefficient in the y direction, and (c) represents the absolute error curve between the test result and the true value of the drag torque loss coefficient in the z direction.

[0064] Figure 6 The figure shows the absolute error curves of the test results and the true values ​​of the rotational inertia loss coefficient of the LSTM neural network in the x, y, and z directions. In the figure, (a) represents the absolute error curve of the test results and the true values ​​of the rotational inertia loss coefficient in the x direction, (b) represents the absolute error curve of the test results and the true values ​​of the rotational inertia loss coefficient in the y direction, and (c) represents the absolute error curve of the test results and the true values ​​of the rotational inertia loss coefficient in the z direction.

[0065] Figure 7 This is a graph showing the absolute error between the test results and the true values ​​of the LSTM neural additional mass loss coefficient in the xyz direction of the present invention.

[0066] In the figure, (a) represents the absolute error curve between the test results and the true value of the additional mass loss coefficient in the x direction, (b) represents the absolute error curve between the test results and the true value of the additional mass loss coefficient in the y direction, and (c) represents the absolute error curve between the test results and the true value of the additional mass loss coefficient in the z direction.

[0067] Figure 8This is a graph showing the absolute error between the training results and the true values ​​of the drag loss coefficient of the LSTM neural network in the xyz direction according to the present invention.

[0068] In the figure, (a) represents the absolute error curve between the training result and the true value of the resistance loss coefficient in the x direction, (b) represents the absolute error curve between the training result and the true value of the resistance loss coefficient in the y direction, and (c) represents the absolute error curve between the training result and the true value of the resistance loss coefficient in the z direction.

[0069] Figure 9 This is a graph showing the absolute error between the training results and the true values ​​of the drag torque loss coefficient of the LSTM neural network of the present invention in the xyz direction;

[0070] In the figure, (a) represents the absolute error curve between the training result and the true value of the resistance torque loss coefficient in the x direction, (b) represents the absolute error curve between the training result and the true value of the resistance torque loss coefficient in the y direction, and (c) represents the absolute error curve between the training result and the true value of the resistance torque loss coefficient in the z direction.

[0071] Figure 10 The figure shows the absolute error curves of the training results and the true values ​​of the rotational inertia loss coefficients of the LSTM neural network in the xyz direction; (a) in the figure represents the absolute error curve of the training results and the true values ​​of the rotational inertia loss coefficients in the p direction, (b) represents the absolute error curve of the training results and the true values ​​of the rotational inertia loss coefficients in the q direction, and (c) represents the absolute error curve of the training results and the true values ​​of the rotational inertia loss coefficients in the r direction.

[0072] Figure 11 This is a graph showing the absolute error between the training results and the true values ​​of the LSTM neural network with the added quality loss coefficients in the xyz directions.

[0073] In the figure, (a) represents the absolute error curve between the training result and the true value with the added mass loss coefficient in the x direction, (b) represents the absolute error curve between the training result and the true value with the added mass loss coefficient in the y direction, and (c) represents the absolute error curve between the training result and the true value with the added mass loss coefficient in the z direction.

[0074] Figure 12 This is a curve comparing the position tracking error of the quadcopter UAV of the present invention with the tracking effect of the traditional method; in the figure, (a) represents the curve comparing the position tracking error of the x-axis, (b) represents the curve comparing the position tracking error of the y-axis, and (c) represents the curve comparing the position tracking error of the z-axis.

[0075] Figure 13The figure shows a comparison of the attitude angle error of the quadcopter UAV of the present invention with the control effect of traditional methods; (a) in the figure represents the comparison curve of pitch angle and desired angle error, (b) represents the comparison curve of roll angle and desired angle error, and (c) represents the comparison curve of yaw angle and desired angle error. Detailed Implementation

[0076] 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 a part of the embodiments of the present invention, and not all of them. 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. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0077] Specific implementation method one: Refer to Figure 1 This embodiment specifically describes a cross-medium vehicle control method based on adaptive LSTM and Tube MPC, comprising:

[0078] Step 1: Based on the forces and moments acting on the vehicle during the cross-medium process, and in conjunction with the Newton-Euler equations, obtain the cross-medium dynamics model of the vehicle.

[0079] The forces and torques experienced by the aircraft during the cross-medium process include at least the additional mass force and torque, restoring force and torque, fluid resistance and torque, control force and torque, and Coriolis force and torque;

[0080] Step 2: Based on the altitude sensor and attitude sensor, obtain the real-time attitude of the vehicle, and use the real-time attitude of the vehicle to calculate the sequence of the vehicle's immersion degree;

[0081] A pre-trained adaptive LSTM fluid parameter predictor is used, with the sequence of vehicle submersion as input, to obtain time-varying fluid parameters;

[0082] Step 3: Input the time-varying fluid parameters into the transmedium dynamics model of the vehicle to obtain the updated transmedium dynamics model of the vehicle;

[0083] Step 4: Based on the updated dynamic model and the Tube MPC robust controller, the control command at the current moment is obtained by using the real-time attitude and desired attitude of the vehicle.

[0084] The Tube MPC robust controller is configured as: the same nominal model and auxiliary state feedback controller as the updated dynamics model;

[0085] The nominal model is subjected to constraints that have been compressed based on the minimum robust positive invariant set. The desired attitude is then used to solve the finite-time optimal control problem to obtain the nominal control quantity.

[0086] The auxiliary state feedback controller calculates the deviation between the real-time attitude and the nominal attitude at the corresponding time, restricts the deviation to an invariant compact set, and obtains the auxiliary feedback quantity; the nominal attitude is the attitude of the nominal model.

[0087] The nominal control quantity and the auxiliary feedback quantity together constitute the final control command.

[0088] Furthermore, in this embodiment, in step one, the transmedium dynamics model of the vehicle is as follows:

[0089]

[0090] in, and For the mass and inertia of the aircraft itself, Indicates added mass. Indicates the additional inertia. Indicates resilience, Indicates restoring torque. This indicates the resistance experienced by the aircraft. Indicates the resistance torque. Indicates control. Indicates control torque. and This represents the force and torque exerted by the Coriolis force on the aircraft; and These represent the linear velocity derivative and angular velocity derivative in the object coordinate system fixed to the vehicle, respectively.

[0091] Furthermore, in this invention, the restoring force for:

[0092]

[0093]

[0094] in, and These represent the forces of gravity and buoyancy acting on the spacecraft, respectively. This represents the rotation matrix that transforms the vehicle from the object coordinate system to the inertial coordinate system.

[0095] In the object's coordinate system, the lever arm of gravity is 0, so only buoyancy needs to be considered. The torque generated by the action;

[0096] This is the restoring torque. :

[0097]

[0098] in, It is the buoyancy lever arm.

[0099] Furthermore, in this embodiment, the resistance experienced by the aircraft... and resistance torque for:

[0100]

[0101] in, Indicates the drag loss coefficient. This represents the drag torque loss coefficient. This represents the drag force experienced by the aircraft in the X-axis direction. This represents the drag force experienced by the aircraft in the Y-axis direction. This represents the drag force experienced by the aircraft in the Z-axis direction. Indicates the impact on the aircraft The torque of the axial resistance. Indicates the impact on the aircraft The torque of the axial resistance. Indicates the impact on the aircraft The torque of the resistance in the axial direction.

[0102] Furthermore, in this embodiment, the force and torque exerted by the Coriolis force on the aircraft... and Represented as:

[0103]

[0104] in, and For the mass and inertia of the aircraft itself, Represents the angular velocity in degrees within a coordinate system fixed to the aircraft. This represents the linear velocity of an object in a coordinate system fixed to the vehicle.

[0105] Furthermore, in this embodiment, control force and control torque They are respectively:

[0106]

[0107] in, Indicates four propellers in The total thrust generated in the direction, These represent the four propellers orbiting each other. The torque of the shaft; specifically expressed as:

[0108]

[0109] In the formula, Indicates the arm length of the aircraft. yes and The ratio, and These are the propeller's thrust coefficient and power coefficient, respectively. , , and These represent the thrust of the four propellers.

[0110] Furthermore, in this embodiment, the method for calculating the sequence of the vehicle's immersion degree using the vehicle's real-time attitude in step two is as follows:

[0111] The altitude of the vehicle's center of gravity relative to the water surface is obtained in real time using altitude and attitude sensors. Euler angles of the aircraft Then calculate the immersion degree at time t. ;

[0112]

[0113] in, This indicates the height of the vehicle's center of mass relative to the water surface. Indicates the pitch angle of the aircraft. H represents the roll angle of the aircraft, and H represents the altitude of the aircraft. This represents the yaw angle of the aircraft, and the sequence of the aircraft's immersion degrees at each discrete time step t. for:

[0114]

[0115] in, The sequence length;

[0116]

[0117] Where N represents the total number of discrete time steps.

[0118] Furthermore, in this embodiment, in step three, the time-varying fluid parameters are:

[0119]

[0120] in, Represents the target fluid parameter vector. , , These represent the mass loss coefficients of the aircraft in the x, y, and z directions, respectively. These respectively indicate that the aircraft is in The coefficient of rotational inertia loss in the direction of rotation. They represent the aircraft. Drag loss coefficient in the direction, These respectively indicate that the aircraft is in The coefficient of resistance torque loss on the rotating shaft.

[0121] Furthermore, in this embodiment, in step three, the finite-time optimal control problem is expressed as:

[0122]

[0123] in, It controls the rate of change (increment) of the input. Indicates in Time Prediction The nominal state vector at time 1. This indicates predicting the control input at time k+i at time k. This indicates predicting the control input at time k+i-1 at time k. This represents the weighted Euclidean norm square. These are the prediction time domains, satisfying... , Represents the spatial domain of the prediction. These are the state tracking error weight matrix and the control input rate of change weight matrix, respectively. This is the terminal state weight matrix; This indicates the prediction at time k. The nominal state vector at time 1. Represents the expected value at time k. The reference state vector at time t.

[0124] Furthermore, in this embodiment, the constraints after compression based on the minimum robust positive invariant set are:

[0125]

[0126] in, , , Represents an invariant compact set, the actual system state Compared with nominal condition Deviation between , The discretized dynamic equations representing LSTM enhancement This represents the predicted value of the actual system state at time k+1 based on the value at time k. This represents the external disturbance term at time k+i. This represents the state constraint after compression. This represents the compressed input constraints. This represents the tightened input rate of change constraint. This indicates the rate of change of the control input.

[0127] This invention proposes an attitude control method for a quadrotor aircraft during a trans-water and trans-air process based on adaptive neural networks (LSTM) and model predictive control (MPC). The overall control framework diagram is shown below. Figure 2 As shown, the dynamic model parameters of the vehicle during the cross-domain process are predicted by a neural network, which ensures the attitude stability of the vehicle during the cross-domain process.

[0128] Step 1: Establish a unified cross-medium dynamics model;

[0129] Considering the additional mass (inertia) of the vehicle during the transdomain process, the additional mass force and torque acting on the vehicle are:

[0130]

[0131] in, and These represent the force and torque exerted on the spacecraft by the added mass (inertia) during transdomain operations, respectively. and They represent the linear velocities in the object coordinate system fixed to the vehicle. The derivatives of and angular velocity, and This represents the added mass and inertia. The added mass (inertia) varies with the submersion degree of the aircraft and is a loss coefficient when represented in the mathematical model as a transdomain event. and The impact is that the loss coefficient is predicted by the neural network LSTM.

[0132] When a spacecraft travels across a region, it is subjected to gravity and buoyancy. In the mathematical model, these forces are defined as restoring force and torque. The expression for the restoring force can be obtained as follows:

[0133]

[0134] in Indicates resilience, and These represent the forces of gravity and buoyancy acting on the spacecraft, respectively. This is the rotation matrix that transforms the vehicle from the object coordinate system to the inertial coordinate system.

[0135] In the object's coordinate system, the lever arm of gravity is 0, so only buoyancy needs to be considered. The torque generated by the action is the restoring torque. :

[0136]

[0137] in, It is the buoyancy lever arm.

[0138] For low-speed underwater vehicles, the Reynolds number is low, and the drag is mainly frictional drag. The mathematical model defines the cross-medium drag (torque) loss coefficient as follows: and Because the drag loss coefficient and drag moment coefficient change constantly when moving in a wave environment, drag can cause unpredictable disturbances to the motion of the aircraft. This indicates that the aircraft experiences resistance in a fluid. The resistance torque represents the effect of resistance. The resistance and resistance torque in a certain degree of freedom can be obtained by the following formula:

[0139]

[0140] In the formula, It is a dimensionless drag coefficient related to the Reynolds number Re, which can be obtained by examining the cylinder drag curve. It is the speed of the aircraft relative to the incoming current. It is the total surface area of ​​the aircraft. It is the density of water.

[0141] Define the drag loss coefficient drag torque loss coefficient The drag loss coefficient is predicted by LSTM. Therefore, the drag and torque experienced by the vehicle during the cross-medium process are expressed as:

[0142]

[0143] The control forces and moments for a quadcopter during transdomain processes are expressed as follows:

[0144]

[0145] in It is the density of the medium in which the i-th propeller is located, assuming the propeller is operating in air or still water. and Represents the rotational speed and diameter of the i-th propeller. It is the lead speed coefficient, which is related to the propeller speed and its axial movement speed relative to the incoming flow. and These are the propeller's thrust coefficient and power coefficient, respectively, which are related to parameters such as the propeller's blade shape, rotational speed, and propulsion speed. Since the simulation focuses on low-speed motion, the thrust variation during the transverse motion is mainly caused by changes in the medium density and rotational speed; therefore, the thrust coefficient is neglected. right and The impact of the propeller of And can be considered as constants that do not change with rotational speed. The four propellers in Total thrust generated in the direction and around Shaft torque It can be calculated from the thrust distribution matrix below:

[0146]

[0147] In the formula It is the arm length of the aircraft. yes and The ratio. Set the control force vector and control torque vector in the object coordinate system as:

[0148]

[0149] The spacecraft is subject to the Coriolis force, which is expressed as:

[0150]

[0151] in, and For the mass and inertia of the aircraft itself, and This represents the force and torque exerted by the Coriolis force on the aircraft.

[0152] The above mathematical model characterizes the main forces and torques acting on the aircraft during transdomain operations, based on which a dynamic model of the aircraft can be established:

[0153]

[0154] To date, the force (torque) components of the aircraft have been fully derived. A trans-domain dynamic model of the aircraft in the object coordinate system has been established using the Newton-Euler equations.

[0155] Step 2: Construct an adaptive LSTM fluid parameter predictor;

[0156] Firstly, the altitude and attitude sensors can be used to determine the real-time height of the vehicle's center of gravity relative to the water surface. Euler angles of the aircraft The immersion level can be calculated. for:

[0157]

[0158] At each discrete time step t, the input sequence is defined. for:

[0159]

[0160] in The sequence length depends on the size of the training data. Adaptive determination

[0161]

[0162] The predictor output is a 12-dimensional target fluid parameter vector. ,

[0163]

[0164] The first six parameters are the additional mass loss coefficients, and the last six parameters are the damping loss coefficients.

[0165] Considering the variability of data scale in practical applications, this design employs an adaptive deep LSTM network architecture. When the number of training samples is sufficiently large (N≥50), a standard network structure is used to provide stronger feature learning capabilities: this structure includes a 16-unit LSTM layer, followed by two fully connected layers (containing 32 and 24 neurons respectively), with ReLU activation and dropout regularization (at a ratio of 0.1) introduced between layers, and finally a 12-dimensional output layer for multivariate regression prediction. When the number of samples is limited (N<50), a simplified network structure is used to avoid overfitting: this structure includes an 8-unit LSTM layer, followed by a 16-neuron fully connected layer and a ReLU activation function, and finally a 12-dimensional output layer for prediction. This adaptive design is as follows: Figure 3 .

[0166] Network parameters Optimization is performed by minimizing the composite loss function. Considering the differences in the dimensions of the output parameters, a weighted mean squared error loss is used.

[0167]

[0168] in For batch size, This is a balancing coefficient, adjusted according to the relative importance of the output parameters. For the first The first sample The actual and predicted values ​​of each parameter.

[0169] Training uses the Adam optimizer, whose parameter update rules are as follows:

[0170]

[0171] Key parameter settings: Initial learning rate Momentum parameters Numerical stability constant The learning rate adopts a segmented decay strategy, with a decay factor of 0.5 every 100 training cycles.

[0172] The trained LSTM network is then encapsulated as a lightweight prediction module and integrated into the MPC control loop. In each control cycle, the MPC controller inputs the maintained immersion sequence into this module to obtain real-time fluid parameter predictions and update the dynamic model. This design enables the controller to adaptively compensate for nonlinear hydrodynamic effects caused by abrupt changes in the medium, significantly improving the control performance of cross-domain processes.

[0173] Step 3: Design and implement an LSTM-enhanced Tube-MPC controller;

[0174] Considering the six degrees of freedom motion of the aircraft, the system state vector is defined as:

[0175]

[0176] in Includes position and Euler angles, and velocity vector in body coordinates. It includes linear velocity and angular velocity components.

[0177] The LSTM-enhanced continuous-time dynamics model can be expressed as:

[0178]

[0179] in To control the input vector, Given a time-varying fluid parameter vector, the LSTM real-time parameter prediction module provides the time-varying fluid parameters based on sensor data:

[0180]

[0181] in This is a historical sequence of immersion levels calculated in real time using altitude and attitude sensors. These are the optimal parameters for the trained LSTM network. These parameters are updated in real-time with the system's additional mass loss coefficients and drag loss coefficients.

[0182] To ensure numerical accuracy, the fourth-order Runge-Kutta method is used to discretize the dynamic model, resulting in a discrete-time prediction model:

[0183]

[0184] in Sampling period, intermediate variable to Calculated by the enhanced dynamics model:

[0185]

[0186] The core idea of ​​Tube MPC is to confine the impact of uncertainty to an invariant "tube"-shaped neighborhood through a master-slave control structure. Using the same nominal system as the LSTM-enhanced dynamics model, but neglecting all prediction errors and disturbances, its dynamic equations are:

[0187]

[0188] in and These are nominal status and nominal input, respectively.

[0189] Secondly, a linear state feedback controller is designed to stabilize the actual system state. Compared with nominal condition Deviation between , will deviation Restricted to an invariant compact set Internally, the controller uses a feedback gain matrix. accomplish:

[0190]

[0191] Ultimately, the control law acting on the actual system is composed of the nominal control quantity and the auxiliary feedback quantity.

[0192] To ensure that the real system can still satisfy the original constraints under uncertainty. , Apply a compressed constraint to the nominal system:

[0193]

[0194] in Describe the difference set of Pontryagin. It is the minimum robust positive invariant set obtained through offline computation, which satisfies:

[0195]

[0196] in For a bounded perturbation set, where Let be the linearized discrete state matrix of the system at the equilibrium point.

[0197] At each sampling time Based on the current nominal status Solve the following finite-time optimal control problem:

[0198]

[0199] in It controls the rate of change (increment) of the input. This is the actual control input from the previous moment. They are respectively the prediction time domain and the control time domain, satisfying , These are the weight matrices for state tracking error and the rate of change of control input, respectively. Terminal weights. The following was obtained by solving the discrete-time algebraic Riccati equation:

[0200]

[0201] in, and These represent the linearized discrete state matrices of the system at the equilibrium point.

[0202] In cross-media tasks, the state and control constraints satisfied at time step k are as follows:

[0203]

[0204] in, , , Represents an invariant compact set, the actual system state Compared with nominal condition Deviation between , The discretized dynamic equations representing LSTM enhancement This represents the predicted value of the actual system state at time k+1 based on the value at time k. This represents the external disturbance term at time k+i. This represents the state constraint after compression. This represents the compressed input constraints. This represents the tightened input rate of change constraint. This indicates the rate of change of the control input.

[0205] Step 4: Perform numerical simulation and performance comparison;

[0206] To verify the effectiveness of the proposed LSTM fluid parameter predictor, this study trained and tested the network based on 1000 sets of hydrodynamic data of cross-medium vehicles (equivalent to cylinders) under different immersion states. The dataset includes the immersion degree and the corresponding 12 fluid parameter values, covering the entire process from complete emergence to complete immersion.

[0207] After removing outliers, 990 valid samples were obtained and adaptively divided into a training set (792 samples), a validation set (99 samples), and a test set (99 samples) according to the data volume. For the data scale, the network adopted an adaptive depth LSTM architecture, configured as a 16-unit LSTM layer connected to a three-layer fully connected network, and a dropout layer (ratio 0.1) was introduced to prevent overfitting. During training, the Adam optimizer was used with an initial learning rate of 0.001, coupled with a piecewise decay strategy. The network training underwent 300 iterations and exhibited good convergence characteristics.

[0208] Secondly, to verify the superiority of the proposed LSTM-MPC control framework in cross-medium processes, this section conducts a comparative simulation study with the classic SMC controller and the traditional MPC controller, simulating the transition tracking of the vehicle from vertical entry into the water to underwater horizontal attitude during cross-medium processes with wave disturbances and time-varying sea states. This simulation environment is closer to real marine operating conditions, aiming to verify the robustness and adaptability of the controller under strong external disturbances.

[0209] Finally, the simulation results were obtained. Figures 4-13 As can be seen from the figure, the prediction errors of each coefficient are small, and the R² value is high. This uniformity of accuracy reflects that the LSTM network effectively captures the physical law of the variation of added mass with immersion depth, providing a reliable parameter estimation basis for the subsequent MPC controller. Figure 12 It can be seen that under the control of ALSTM-TMPC, the vehicle's attitude angles remain relatively stable, vibration is small, and the errors in roll and yaw angles are limited to within ±2-3. Furthermore, overshoot is small and recovery speed is faster. From Figure 13 It can be seen that in terms of position tracking, the ALSTM-TMPC error range in the cross-media stage is within ±0.6 meters, and it can maintain smooth and continuous motion, which is better than MPC and SMC.

[0210] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A cross-medium vehicle control method based on adaptive LSTM and Tube MPC, characterized in that, include: Step 1: Based on the forces and moments acting on the vehicle during the cross-medium process, and in conjunction with the Newton-Euler equations, obtain the cross-medium dynamics model of the vehicle. The forces and torques experienced by the aircraft during the cross-medium process include at least the additional mass force and torque, restoring force and torque, fluid resistance and torque, control force and torque, and Coriolis force and torque; Step 2: Based on the altitude sensor and attitude sensor, obtain the real-time attitude of the vehicle, and use the real-time attitude of the vehicle to calculate the sequence of the vehicle's immersion degree; A pre-trained adaptive LSTM fluid parameter predictor is used, with the sequence of vehicle submersion as input, to obtain time-varying fluid parameters; Step 3: Input the time-varying fluid parameters into the transmedium dynamics model of the vehicle to obtain the updated transmedium dynamics model of the vehicle; Step 4: Based on the updated dynamic model and the Tube MPC robust controller, the control command at the current moment is obtained by using the real-time attitude and desired attitude of the vehicle. The Tube MPC robust controller is configured as: the same nominal model and auxiliary state feedback controller as the updated dynamics model; The nominal model is subjected to constraints that have been compressed based on the minimum robust positive invariant set. The desired attitude is then used to solve the finite-time optimal control problem to obtain the nominal control quantity. The auxiliary state feedback controller calculates the deviation between the real-time attitude and the nominal attitude at the corresponding time, restricts the deviation to an invariant compact set, and obtains the auxiliary feedback quantity; the nominal attitude is the attitude of the nominal model. The nominal control quantity and the auxiliary feedback quantity together constitute the final control command.

2. The cross-medium vehicle control method based on adaptive LSTM and Tube MPC according to claim 1, characterized in that, In step one, the transmedium dynamics model of the aircraft is as follows: in, and For the mass and inertia of the aircraft itself, Indicates added mass. Indicates the additional inertia. Indicates resilience, Indicates restoring torque. This indicates the resistance experienced by the aircraft. Indicates the resistance torque. Indicates control. Indicates control torque. and This represents the force and torque exerted by the Coriolis force on the aircraft; and These represent the linear velocity derivative and angular velocity derivative in the object coordinate system fixed to the vehicle, respectively.

3. The cross-medium vehicle control method based on adaptive LSTM and Tube MPC according to claim 1, characterized in that, resilience for: in, and These represent the forces of gravity and buoyancy acting on the spacecraft, respectively. This represents the rotation matrix that transforms the vehicle from the object coordinate system to the inertial coordinate system. In the object's coordinate system, the lever arm of gravity is 0, so only buoyancy needs to be considered. The torque generated by the action; This is the restoring torque. : in, It is the buoyancy lever arm.

4. The cross-medium vehicle control method based on adaptive LSTM and Tube MPC according to claim 1, characterized in that, Resistance experienced by the aircraft and resistance torque for: in, Indicates the drag loss coefficient. This represents the drag torque loss coefficient. This represents the drag force experienced by the aircraft in the X-axis direction. This represents the drag force experienced by the aircraft in the Y-axis direction. This represents the drag force experienced by the aircraft in the Z-axis direction. Indicates the impact on the aircraft The torque of the axial resistance. Indicates the impact on the aircraft The torque of the axial resistance. Indicates the impact on the aircraft The torque of the resistance in the axial direction.

5. The cross-medium vehicle control method based on adaptive LSTM and Tube MPC according to claim 1, characterized in that, The force and torque exerted by the Coriolis force on a spacecraft and Represented as: in, and For the mass and inertia of the aircraft itself, Represents the angular velocity in degrees within a coordinate system fixed to the aircraft. This represents the linear velocity of an object in a coordinate system fixed to the vehicle.

6. The cross-medium vehicle control method based on adaptive LSTM and Tube MPC according to claim 1, characterized in that, Control and control torque They are respectively: in, Indicates four propellers in The total thrust generated in the direction, These represent the four propellers orbiting each other. The torque of the shaft; specifically expressed as: In the formula, Indicates the arm length of the aircraft. yes and The ratio, and These are the propeller's thrust coefficient and power coefficient, respectively. , , and These represent the thrust of the four propellers.

7. The cross-medium vehicle control method based on adaptive LSTM and Tube MPC according to claim 1, characterized in that, In step two, the method for calculating the sequence of the vehicle's immersion degree using the vehicle's real-time attitude is as follows: The altitude of the vehicle's center of gravity relative to the water surface is obtained in real time using altitude and attitude sensors. Euler angles of the aircraft Then calculate the immersion degree at time t. ; in, This indicates the height of the vehicle's center of mass relative to the water surface. Indicates the pitch angle of the aircraft. H represents the roll angle of the aircraft, and H represents the altitude of the aircraft. This represents the yaw angle of the aircraft, and the sequence of the aircraft's immersion degrees at each discrete time step t. for: in, The sequence length; Where N represents the total number of discrete time steps.

8. The cross-medium vehicle control method based on adaptive LSTM and Tube MPC according to claim 1, characterized in that, In step three, the time-varying fluid parameters are: in, Represents the target fluid parameter vector. , , These represent the mass loss coefficients of the aircraft in the x, y, and z directions, respectively. These respectively indicate that the aircraft is in The coefficient of rotational inertia loss in the direction of rotation. They represent the aircraft. Drag loss coefficient in the direction, These respectively indicate that the aircraft is in The coefficient of resistance torque loss on the rotating shaft.

9. The cross-medium vehicle control method based on adaptive LSTM and Tube MPC according to claim 1, characterized in that, In step three, the finite-time optimal control problem is expressed as: in, It controls the rate of change (increment) of the input. Indicates in Time Prediction The nominal state vector at time t. This indicates predicting the control input at time k+i at time k. This indicates predicting the control input at time k+i-1 at time k. This represents the weighted Euclidean norm square. These are the prediction time domains, satisfying... , Represents the spatial domain of the prediction. These are the state tracking error weight matrix and the control input rate of change weight matrix, respectively. This is the terminal state weight matrix; This indicates the prediction at time k. The nominal state vector at time t. Represents the expected value at time k. The reference state vector at time t.

10. The cross-medium vehicle control method based on adaptive LSTM and Tube MPC according to claim 9, characterized in that, The constraints after compression based on the minimum robust positive invariant set are: in, , , Represents an invariant compact set, the actual system state Compared with nominal condition Deviation between , The discretized dynamic equations representing LSTM enhancement This represents the predicted value of the actual system state at time k+1 based on the value at time k. This represents the external disturbance term at time k+i. This represents the state constraint after compression. This represents the compressed input constraints. This represents the tightened input rate of change constraint. This indicates the rate of change of the control input.

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