Game guidance and control method of ship unmanned aerial vehicle for channel ice condition detection

Abstract

The application discloses a ship unmanned aerial vehicle game guidance and control method for channel ice condition detection, relates to the technical field of ship / unmanned aerial vehicle motion control research, and comprises the following steps: establishing a ship three-degree-of-freedom and unmanned aerial vehicle six-degree-of-freedom nonlinear model; designing a ship expected task point according to an actual route point, and generating an unmanned aerial vehicle task point according to a detection radius of the unmanned aerial vehicle and a water width; taking the task point as an expected coordinate, constructing a local optimal motion strategy between the ship / unmanned aerial vehicle and a virtual body based on a Stackelberg game, and calculating a global optimal motion strategy according to the local optimal motion strategy; designing a position controller, fusing the ship local optimal strategy and real-time position of the unmanned aerial vehicle, and making attitudes of both sides converge through a total controller composed of an attitude virtual controller and an attitude controller; driving the ship and the unmanned aerial vehicle to execute the optimal strategy through a cooperative action of the position and attitude controllers, and realizing cooperative control; and the application can meet the marine engineering demand of high-precision navigation and resistance to marine environment interference.

Description

Technical Field

[0001] This invention relates to the field of ship / UAV motion control research technology, and in particular to a game-theoretic guidance and control method for ship / UAVs for waterway ice condition detection. Background Technology

[0002] Traditional ice detection and navigational capability analysis rely on polar-orbiting satellites, and the ice information obtained is usually not timely. Ship / UAV collaborative systems, however, fully leverage aerial advantages, using UAVs to continuously monitor ice conditions in the waters surrounding the ship in real time. The key challenge in improving the efficiency of UAV ice detection is how to reorganize UAV formations to achieve efficient coverage of the waters around the ship, avoiding overlapping detection areas and redundant monitoring of non-navigable floating ice zones.

[0003] In the field of multi-agent formation control, the core of achieving formation reorganization and change lies in altering the formation structure. Common design approaches include distributed control based on affine transformation, artificial potential field methods based on task allocation, and leader-follower control based on a pre-set formation library, among others. While these existing methods can achieve formation reorganization and change, they all suffer from reliance on manual adjustment, preset timeframes, and preset formations, as well as instability in the movement of the cooperative agents during reorganization. This makes existing formation reorganization methods unsuitable for the complex and ever-changing real-world engineering requirements.

[0004] In control engineering, the controller of a ship / UAV is typically designed directly from the error along a reference path. However, when the initial point of the ship / UAV deviates significantly from the reference path, problems such as slow error convergence and actuator saturation overload arise. Although the artificial potential field method is commonly used in existing methods to plan a smooth trajectory for the ship / UAV to the reference path in real time, this method does not consider factors such as the control input, maneuverability, and inertia of the ship / UAV. The resulting smooth trajectory is not conducive to achieving high-precision tracking of the ship / UAV, therefore, the artificial potential field method is difficult to apply in engineering practice.

[0005] Based on the above analysis, existing ship / UAV formation reorganization control algorithms mainly have the following two shortcomings:

[0006] 1. Existing formation reorganization schemes rely excessively on manual, pre-set adjustments to the formation structure, lacking autonomous and adaptive adjustments to the navigation environment. Therefore, UAVs cannot dynamically reorganize their formations according to ice conditions to achieve more efficient detection and coverage. Furthermore, because formation reorganization requires changes in ship / UAV speeds, it may lead to instability in the formation system.

[0007] 2. Existing ship / UAV control methods typically design controllers directly using the error from the ship / UAV to the reference path. When the initial position of the ship / UAV deviates significantly from the reference path, this can easily lead to problems such as slow convergence, overshoot, and actuator saturation. Summary of the Invention

[0008] This invention provides a game-theoretic guidance and control method for ship-based unmanned aerial vehicles (UAVs) for waterway ice condition detection, in order to overcome the aforementioned technical problems.

[0009] To achieve the above objectives, the technical solution of the present invention is as follows:

[0010] A game-theoretic guidance and control method for ship-based unmanned aerial vehicles (UAVs) for waterway ice condition detection includes:

[0011] S1: The Euler-Lagrange equations are used to construct a three-degree-of-freedom model of the ship and a six-degree-of-freedom nonlinear mathematical model of the UAV, which will be used as the control objects in the future.

[0012] S2: Design ideal ship mission points based on actual ship waypoints; generate UAV mission points based on the relative relationship between the UAV detection radius and the real-time water width.

[0013] S3: Using the ship's mission point and the UAV's mission point as the desired coordinates, based on Stackelberg game, construct the local optimal motion strategies for the ship / UAV and the virtual ship / UAV respectively, and obtain the optimal motion strategy for the ship / UAV based on the local optimal motion strategies of the ship / UAV and the virtual ship / UAV so that the ship / UAV can reach the desired coordinates.

[0014] S4: Construct a ship / UAV position controller based on the optimal motion strategy to converge the actual positions of the ship and UAV to the corresponding task point coordinates;

[0015] S5: Construct a ship / UAV attitude master controller based on the ship's local optimal motion strategy and the UAV's actual position, so that the ship / UAV's attitude converges to the requirements of the optimal motion strategy; the ship / UAV attitude master controller includes an attitude virtual controller and a ship / UAV attitude controller; control the ship and UAV to execute the optimal motion strategy according to the ship / UAV position controller and the ship / UAV attitude master controller, so as to realize the coordinated control of the ship / UAV.

[0016] Furthermore, the Euler-Lagrange equations are used to construct a three-degree-of-freedom model for the ship and a six-degree-of-freedom nonlinear mathematical model for the UAV, including:

[0017] The three-degree-of-freedom model of the ship and the six-degree-of-freedom nonlinear mathematical model of the UAV are shown below:

[0018]

[0019]

[0020] in, and They are respectively ships and the The state matrix of each UAV, where each element represents the ship's position in a fixed coordinate system. axis, Coordinates on the axis and the drone in axis, shaft and Coordinates on the axis; The attitude matrix represents the ship's heading angle and the UAV's roll, pitch, and heading angles, respectively. This is a linear velocity matrix, representing the forward velocity of the ship and the velocity of the UAV along its path. axis, shaft and The speed of the shaft; Represents the ship's drift speed; This is an angular velocity matrix, representing the ship's bow rate and the UAV's roll, pitch, and bow rates, respectively. Let be the quality matrix, where, The mass of the ship in the forward direction, For the quality of the drone; Let be the moment of inertia matrix, representing the mass of the ship in the bow direction and the mass of the UAV along the direction of rotation. axis, axis, Moment of inertia of the shaft; The mass of the vessel in the lateral drift direction; The position control input matrix represents the ship's forward control input and the UAV's position control input. axis, axis, Control inputs on the axis; The attitude control input matrix represents the ship's yaw control input and the UAV's roll, pitch, and yaw control inputs, respectively. This is the gravitational acceleration matrix; This is a position interference matrix, representing the interference experienced by the ship in its forward direction and the interference experienced by the UAV in the following directions. axis, axis, Interference experienced on the axis; The attitude interference matrix represents the interference experienced by the ship in the bow direction and the interference experienced by the UAV in the roll, pitch, and bow directions, respectively. The position nonlinearity matrix represents the system nonlinear parameters of the ship in the forward direction and the UAV in the direction of travel, respectively. axis, axis, Nonlinear parameters of the system on the axis; For attitude nonlinear parameters, denoted as the system nonlinear parameters of the ship in the yaw direction and the system nonlinear parameters of the UAV in the heel, pitch, and yaw directions, respectively. For the system nonlinear parameters of the ship in the lateral drift direction;

[0021] in,

[0022]

[0023] These respectively represent the drones in axis, axis, Nonlinear parameters in the axial, tilt, pitch, and yaw directions; These are the moment of inertia and rotational speed of the UAV rotor, respectively. These are the first, second, and third order parameters of the nonlinear system for the ship's forward direction, respectively. These are the first, second, and third order parameters of the nonlinear system in the lateral drift direction of the ship, respectively. These are the first, second, and third order parameters of the ship's bow roll direction nonlinear system, respectively.

[0024] Furthermore, based on actual ship waypoints, ideal ship mission points are designed, including:

[0025] Definition of the first The waypoints and their coordinates are as follows: The preceding and following waypoints and their coordinates are represented as follows: and , ;

[0026] Define a first straight navigation segment, a second straight navigation segment, and a turning segment between three consecutive waypoints; define task points located in the two straight navigation segments and the two task points located in the turning segment.

[0027] Case 1: If the current segment is a straight navigation segment, then the ship's mission points for the first and second straight navigation segments are obtained based on the waypoints. The expressions for the ship's mission points are as follows:

[0028]

[0029] in, The ship's mission points axis, Axis coordinates, heading angle, forward speed, and roll speed; definitions This is the state matrix of the ship's mission points; the initial state of the ship's mission points is set as follows: ;

[0030] When the ship's mission point is located on the first straight segment of navigation, it is defined as follows: and for:

[0031]

[0032] When the ship's mission point is located on the second straight segment of navigation, it is defined as follows: and for:

[0033] ;

[0034] in, and These are the headings for the first and second straight sections of the straight route, respectively.

[0035] Case 2: If the current segment is a turning segment, then define for:

[0036]

[0037] in, This represents the difference in heading between the second straight-line navigation segment and the first straight-line navigation segment. ; The turning radius is expressed as follows:

[0038]

[0039] in, and These are the maximum turning radius and the minimum turning radius, respectively.

[0040] Based on the turning radius, the ship's mission point and waypoint for the straight navigation segment, the expression for the mission point of the turning segment is as follows:

[0041]

[0042] in, for and The coordinates of the mission points for the turning segments between them. for and The coordinates of the mission points for the turning segments between them;

[0043] Furthermore, based on the relative relationship between the UAV's detection radius and the real-time water width, UAV mission points are generated, including:

[0044] Step 1: Determine the width of the navigable area Size:

[0045] When both sides of the ship's drones detect unnavigable areas, i.e., areas of floating ice, the width of the navigable area is... The value can have the following possibilities:

[0046] Scenario 1: When When designing the distribution formula for UAV mission points, the formula is:

[0047]

[0048] in, For formation reorganization parameters;

[0049] Scenario 2: When When designing the distribution formula for UAV mission points, the formula is:

[0050]

[0051] in, To assist in calculating parameters, ;

[0052] Scenario 3: When When designing the distribution formula for UAV mission points, the formula is:

[0053]

[0054] in, ;

[0055] Scenario 4: When When designing the distribution formula for UAV mission points, the formula is:

[0056]

[0057] in, ;

[0058] Scenario 5: When When designing the distribution formula for UAV mission points, the formula is:

[0059]

[0060] When neither of the drones on either side of the ship can detect the unnavigable area, the values ​​used to determine the detection range of the drone formation can fall into the following categories:

[0061] Scenario 1: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with ;

[0062] Scenario 2: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with , Replace with ;

[0063] Scenario 3: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with ;

[0064] Scenario 4: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with ;

[0065] When only one side of the ship's drones detects an unnavigable area, i.e. the drones cannot obtain the width of the navigable waters, the drone formation maintains its current formation until both sides of the ship's drones detect an unnavigable area or neither can detect an unnavigable area, at which point the distribution of drone mission points is calculated.

[0066] Step 2: Based on the distribution of UAV mission points, define the mathematical expression for each UAV mission point as follows:

[0067]

[0068] in, This is a state matrix for UAV mission points, representing the UAV mission points respectively. axis, axis, Axis coordinates; Represents a rotation matrix; This represents the relative position of the UAV mission point to the ship mission point, forming a formation matrix.

[0069] Furthermore, using the ship's mission point and the UAV's mission point as the desired coordinates, and based on Stackelberg game theory, locally optimal motion strategies for the ship / UAV and the virtual ship / UAV are constructed respectively, including:

[0070] S31. Constructing locally optimal motion strategies for ships / UAVs based on Stackelberg game theory:

[0071] The performance metrics for the follower layer in the Stackelberg game between ships / drones and virtual ships / drones are as follows:

[0072]

[0073] in, This represents the performance metrics of the follower layer. Represents time, To account for the error between the ship / drone and the virtual ship / drone, For the ship / UAV state matrix, For virtual state matrix, These are the motion strategies employed by ships / drones and virtual ships / drones, respectively. Both are positive symmetric matrices, representing ships / drones and virtual ships / drones respectively. The weight it occupies in the middle;

[0074] Based on the principles of differential game theory, construct a system that... The local optimal motion strategy for ships / UAVs with the minimum value is:

[0075]

[0076] in, for The minimum value, for The estimated value; The local optimal motion strategy for the ship / UAV is given by, where, These are the local optimal motion strategies for ships and drones, respectively. for The estimated value; where, They are respectively The estimated value; These are the weights and activation functions of a radial basis function neural network, respectively. They are respectively The critic and actor estimates; For ship / UAV kinematic control, the control parameter matrix is ​​provided.

[0077] S32. Based on Stackelberg game theory, construct the local optimal motion strategy for the virtual ship / machine:

[0078] The leadership performance metrics for designing a Stackelberg game between ships / drones and virtual ships / drones are:

[0079]

[0080] in, Represents leadership performance indicators; The error between the virtual ship / aircraft and the mission point; Both are positive symmetric matrices, representing virtual ships / aircraft and ships / drones respectively. The weight it occupies in the middle; The task matrix represents the desired formation, i.e., the desired coordinates of ships / UAVs;

[0081] Based on the principles of differential game theory, construct a system that... The local optimal motion strategy for the virtual ship / machine with the minimum value is:

[0082]

[0083] in, for The minimum value, Then it is The estimated value; The local optimal motion strategy for the virtual ship / machine. Its estimated value; These are the weights and activation functions of a radial basis function neural network, respectively. They are respectively The critic and actor estimates; This is the control parameter matrix for virtual ship / machine kinematic control.

[0084] Furthermore, the optimal motion strategy for the ship / UAV is obtained based on the local optimal motion strategies of the ship / UAV and the virtual ship / UAV, including:

[0085] By combining the local optimal motion strategies of the ship / UAV and the virtual ship / UAV, the estimated value of the local optimal motion strategy of the ship / UAV is obtained, that is, the optimal motion strategy of the ship / UAV is:

[0086]

[0087] Construct an update law for the weight estimates of the neural network so that... Converging to ; Converging to ,make Converging to The update law is as follows:

[0088]

[0089] in, It is the identity matrix. All are positive constants, representing respectively Update rate; A positive constant represents the minimum update law.

[0090] Furthermore, a ship / UAV position controller is constructed based on the optimal motion strategy, including:

[0091] S41. Define the expression for the virtual position control through a first-order filter as follows:

[0092]

[0093] in, for The time constant of the first-order low-pass filter ; for The filtered signal;

[0094] S42. The expression for position dynamics error and its derivative is defined as follows:

[0095]

[0096]

[0097] S43. Based on the position dynamics error and its derivative, a ship / UAV position controller is constructed as follows:

[0098]

[0099] in, For the position control parameter matrix, Here, represents the weights and activation function of the positional radial basis function neural network, used to approximate the positional nonlinear matrix. ; for The estimated value; Position interference matrix The observed values ​​are shown below:

[0100]

[0101] in, For location interference observation parameters; For location interference auxiliary parameters; The update law is:

[0102]

[0103] In the formula, All are positive diagonal matrices, representing respectively The update rate and its minimum update law.

[0104] Furthermore, a ship / UAV attitude master controller is constructed based on the ship's local optimal motion strategy and the UAV's actual position, including:

[0105] S51. Local Optimal Motion Strategy Based on Ship and drone position control input The ship / UAV reference attitude is calculated as follows:

[0106]

[0107] in, This is the ship / UAV reference attitude matrix, representing the ship's reference heading angle and the UAV's reference roll, pitch, and heading angles, respectively; where, This is the default value; Representing matrices respectively The first and second row elements; Represents the lift of the drone;

[0108] S52. Define the kinematic error of ship / UAV attitude as:

[0109]

[0110] A virtual attitude controller is constructed based on the kinematic errors of ship / UAV attitude:

[0111]

[0112] in, For attitude virtual controller; A positive symmetric matrix, representing the attitude virtual control parameter matrix;

[0113] S53. The attitude virtual controller is filtered using a first-order low-pass filter to obtain... ;

[0114]

[0115] In the formula, for The time constant of the first-order low-pass filter for The filtered signal;

[0116] The attitude dynamics error is defined as:

[0117]

[0118] A ship / UAV attitude controller is constructed based on attitude dynamics errors as follows:

[0119]

[0120] In the formula, This is the attitude control parameter matrix; These are the weights and activation functions of the attitude radial basis function neural network, used to approximate the position nonlinear matrix. ; for The estimated value; Attitude disturbance matrix The observed values ​​are shown below.

[0121]

[0122] In the formula, For attitude disturbance observation parameters; For attitude disturbance auxiliary parameters;

[0123] also, The update law can be expressed as

[0124]

[0125] In the formula, All are positive diagonal matrices, representing respectively The update rate and its minimum update law.

[0126] Beneficial effects: This invention provides a game-theoretic guidance and control method for ship-based unmanned aerial vehicles (UAVs) for waterway ice condition detection, which has the following advantages:

[0127] 1. The ship / UAV game-theoretic optimization guidance and control technology of this invention solves the problems of ship / UAV navigation and ice condition detection in polar waterways. The established ship / UAV mission points can not only plan navigation routes for ships / UAVs, but also autonomously change the UAV's detection formation based on the detected water environment, thereby achieving more efficient detection coverage of the waters surrounding the ship and more accurate ice condition detection. Compared with existing formation reorganization or switching schemes that rely on manual manipulation or preset conditions, the formation reorganization method designed in this invention is more flexible and can adapt to the complex and ever-changing actual marine engineering needs.

[0128] 2. The ship / UAV formation cooperative control proposed in this invention, based on Stackelberg game theory, solves the problem of ships / UAVs being far from the mission point at their initial position. By using Stackelberg game theory, the optimal virtual motion strategy for ships / UAVs is solved to efficiently guide them to the mission point, and the optimal motion strategy for ships / UAVs is further solved to achieve rapid convergence. Compared with existing control methods, the control method proposed in this invention has faster convergence, stronger robustness, and higher control accuracy, and is better able to meet the needs of high-precision navigation and marine engineering requiring resistance to marine environmental interference. Attached Figure Description

[0129] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0130] Figure 1 The flowchart of the game-theoretic guidance and control method for ship-based UAVs for waterway ice condition detection provided by the present invention is shown below.

[0131] Figure 2 Schematic diagram of ship / drone formation;

[0132] Figure 3 A diagram illustrating the reorganization of ship / drone formations;

[0133] Figure 4 A schematic diagram showing the navigation trajectory and detection coverage results of a ship / UAV collaborative system in narrow polar waterways;

[0134] Figure 5 This is a schematic diagram of the position error results for ships / UAVs.

[0135] Figure 6 This is a schematic diagram of the linear velocity results for the drone.

[0136] Figure 7 This is a schematic diagram showing the results of the UAV reconstructed detection formation.

[0137] Figure 8 This is a schematic diagram of the results of ocean interference observations;

[0138] Figure 9 This is a schematic diagram showing the ship path tracking results under the present invention and existing control algorithms;

[0139] Figure 10 This is a schematic diagram showing the ship path tracking error results under the present invention and existing control algorithms. Detailed Implementation

[0140] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0141] This embodiment provides a game-theoretic guidance and control method for ship-based unmanned aerial vehicles (UAVs) for waterway ice condition detection, such as... Figure 1 As shown, it includes:

[0142] S1: The Euler-Lagrange equations are used to construct a three-degree-of-freedom model of the ship and a six-degree-of-freedom nonlinear mathematical model of the UAV, which will be used as the control objects in the future.

[0143] S2: Design ideal ship mission points based on actual ship waypoints; generate UAV mission points based on the relative relationship between the UAV detection radius and the real-time water width.

[0144] S3: Using the ship's mission point and the UAV's mission point as the desired coordinates, based on Stackelberg game, construct the local optimal motion strategies for the ship / UAV and the virtual ship / UAV respectively, and obtain the optimal motion strategy for the ship / UAV based on the local optimal motion strategies of the ship / UAV and the virtual ship / UAV so that the ship / UAV can reach the desired coordinates.

[0145] S4: Construct a ship / UAV position controller based on the optimal motion strategy to converge the actual positions of the ship and UAV to the corresponding task point coordinates;

[0146] S5: Construct a ship / UAV attitude master controller based on the ship's local optimal motion strategy and the UAV's actual position, so that the ship / UAV's attitude converges to the requirements of the optimal motion strategy; the ship / UAV attitude master controller includes an attitude virtual controller and a ship / UAV attitude controller; control the ship and UAV to execute the optimal motion strategy according to the ship / UAV position controller and the ship / UAV attitude master controller, so as to realize the coordinated control of the ship / UAV.

[0147] Specifically, considering the requirements of "complex and variable ice conditions" and "high-precision collaborative navigation between ships and UAVs" in actual polar waterway ice condition detection missions, this invention proposes a ship / UAV game-theoretic optimization guidance and control technology for waterway ice condition detection missions. By dynamically reorganizing and changing UAV formations, the detection coverage efficiency of the water environment surrounding ships is improved. This technology includes two modules: guidance and control, and has the following characteristics:

[0148] For the guidance module, this invention first designs ship mission points along waypoints to guide ships through narrow channels. Then, it categorizes the UAV's detection of the navigation area into three types, optimizes the UAV formation structure for each, and designs UAV mission points based on ship mission points and UAV formation reconfiguration characteristics. This results in a ship / UAV guidance signal that can both coordinate navigation in narrow channels and reconfigure its formation according to the detected water environment.

[0149] For the control module, this invention constructs a ship / UAV control method based on Stackelberg game theory. This method introduces a virtual ship / UAV and treats the virtual ship / UAV and the actual ship / UAV as two types of players in a Stackelberg game. This allows for the solution of the optimal motion strategy for the virtual ship / UAV, efficiently guiding the ship / UAV to its mission point, and simultaneously solving for the optimal motion strategy for the ship / UAV, accelerating its convergence to the virtual ship / UAV.

[0150] In a specific embodiment, the Euler-Lagrange equations are used to construct a three-degree-of-freedom model of the ship and a six-degree-of-freedom nonlinear mathematical model of the UAV, which serves as the subsequent control object.

[0151] The three-degree-of-freedom model of the ship and the six-degree-of-freedom nonlinear mathematical model of the UAV are shown below:

[0152]

[0153]

[0154] in, and They are respectively ships and the The state matrix of each UAV, where each element represents the ship's position in a fixed coordinate system. axis, Coordinates on the axis and the drone in axis, shaft and Coordinates on the axis; The attitude matrix represents the ship's heading angle and the UAV's roll, pitch, and heading angles, respectively. This is a linear velocity matrix, representing the forward velocity of the ship and the velocity of the UAV along its path. axis, shaft and The speed of the shaft; Represents the ship's drift speed; This is an angular velocity matrix, representing the ship's bow rate and the UAV's roll, pitch, and bow rates, respectively. Let be the quality matrix, where, The mass of the ship in the forward direction, For the quality of the drone; Let be the moment of inertia matrix, representing the mass of the ship in the bow direction and the mass of the UAV along the direction of rotation. axis, axis, Moment of inertia of the shaft; The mass of the vessel in the lateral drift direction; The position control input matrix represents the ship's forward control input and the UAV's position control input. axis, axis, Control inputs on the axis; The attitude control input matrix represents the ship's yaw control input and the UAV's roll, pitch, and yaw control inputs, respectively. This is the gravitational acceleration matrix; This is a position interference matrix, representing the interference experienced by the ship in its forward direction and the interference experienced by the UAV in the following directions. axis, axis, Interference experienced on the axis; The attitude interference matrix represents the interference experienced by the ship in the bow direction and the interference experienced by the UAV in the roll, pitch, and bow directions, respectively. The position nonlinearity matrix represents the system nonlinear parameters of the ship in the forward direction and the UAV in the direction of travel, respectively. axis, axis, Nonlinear parameters of the system on the axis; For attitude nonlinear parameters, denoted as the system nonlinear parameters of the ship in the yaw direction and the system nonlinear parameters of the UAV in the heel, pitch, and yaw directions, respectively. For the system nonlinear parameters of the ship in the lateral drift direction;

[0155] in,

[0156]

[0157] These respectively represent the drones in axis, axis, Nonlinear parameters in the axial, tilt, pitch, and yaw directions; These are the moment of inertia and rotational speed of the UAV rotor, respectively. These are the first, second, and third order parameters of the nonlinear system for the ship's forward direction, respectively. These are the first, second, and third order parameters of the nonlinear system in the lateral drift direction of the ship, respectively. These are the first, second, and third order parameters of the ship's bow roll direction nonlinear system, respectively.

[0158] In a specific embodiment, an ideal ship mission point is designed based on actual ship waypoints; the scheme for generating UAV mission points is as follows, based on the relative relationship between the UAV's detection radius and the real-time water width:

[0159] like Figure 2 The diagram illustrates the principle of ship / UAV formation. Figure (a) shows a 3D view, and (b) shows a 2D view. The desired formation of the ship / UAV formation is composed of mission points. Ship mission points are automatically generated from preset waypoints to guide coordinated ship / UAV navigation. UAV mission points depend on the navigation water environment detected by the UAVs, aiming to form a UAV detection formation adapted to the water features and improve the detection efficiency of the water environment near ships. The specific steps are as follows:

[0160] Step 1: Define the first The waypoints and their coordinates are as follows: The preceding and following waypoints and their coordinates are represented as follows: and , ;

[0161] Define a first straight navigation segment, a second straight navigation segment, and a turning segment between three consecutive waypoints; define task points located in the two straight navigation segments and the two task points located in the turning segment.

[0162] Specifically, firstly, we define the first The waypoints and their coordinates are as follows: The preceding and following waypoints and their coordinates are represented as follows: and , It is desired that ships navigate along the routes formed by connecting waypoints, passing each waypoint in sequence. However, because ships need to navigate along the routes... and Turning between them, unable to pass through waypoints The vessel's mission points require decision-making regarding the straight-ahead navigation phase and the turning navigation phase, and determining the timing of the turn. Therefore, these are called waypoints. Select two turning points The ship's mission point will be... and The phase guides the ship to navigate in a straight line, and in Phased guidance for ship navigation;

[0163] Step 2: Determine the ship's navigation status:

[0164] Case 1: If the current segment is a straight navigation segment, then the ship's mission points for the first and second straight navigation segments are obtained based on the waypoints. The expressions for the ship's mission points are as follows:

[0165]

[0166] in, The ship's mission points axis, Axis coordinates, heading angle, forward speed, and roll speed; definitions This is the state matrix of the ship's mission points; the initial state of the ship's mission points is set as follows: ; When the initial state of the specified ship mission point Initial heading angle and forward speed Afterwards, it can be changed To modify the status information of the ship's mission point;

[0167] When the ship's mission point is located on the first straight segment of navigation, it is defined as follows: and for:

[0168]

[0169] When the ship's mission point is located on the second straight segment of navigation, it is defined as follows: and for:

[0170] ;

[0171] in, and These are the headings for the first and second straight sections of the straight route, respectively.

[0172] Case 2: If the current segment is a turning segment, then define for:

[0173]

[0174] in, This represents the difference in heading between the second straight-line navigation segment and the first straight-line navigation segment. ; The turning radius is expressed as follows:

[0175]

[0176] in, and These are the maximum turning radius and the minimum turning radius, respectively.

[0177] Based on the turning radius, the ship's mission point and waypoint on the straight navigation segment, the expression for the turning point is as follows:

[0178]

[0179] in, for and The coordinates of the mission points for the turning segments between them. for and The coordinates of the mission points for the turning segments between them;

[0180] Define drones at altitude The detection radius at that time is The drones should be deployed along the sides of the vessel or in the same line as the vessel to detect the surrounding waters. Simultaneously, the drones should be able to dynamically reorganize their formation according to the water environment, and the detection ranges of each drone should not overlap. Figure 3 As shown. Therefore, based on the ship's mission points, and according to the relative relationship between the UAV's detection radius and the real-time water width, UAV mission points are generated, including:

[0181] Step 1: Determine the width of the navigable area Size:

[0182] When both sides of the ship's drones detect unnavigable areas, i.e., areas of floating ice, the width of the navigable area is... The value can have the following possibilities:

[0183] Scenario 1: When At this time, the drone formation should be in Figure 3 (a) to Figure 3 (b) The distribution formula for UAV mission points is as follows:

[0184]

[0185] in, For formation reorganization parameters;

[0186] Scenario 2: When At that time, the drone formation should be in Figure 3 (b) to Figure 3 The distribution formula for UAV mission points is designed based on the states between (c).

[0187]

[0188] in, To assist in calculating parameters, ;

[0189] Scenario 3: When At that time, the drone formation should be in Figure 3 (b) to Figure 3 The distribution formula for UAV mission points is designed based on the states between (c).

[0190]

[0191] in, ;

[0192] Scenario 4: When At that time, the drone formation should be in Figure 3 (b) to Figure 3 The distribution formula for UAV mission points is designed based on the states between (c).

[0193]

[0194] in, ;

[0195] Scenario 5: When At that time, the drone formation should be in Figure 3 In state (d), the formula for the distribution of UAV mission points is:

[0196]

[0197] When neither of the drones on either side of the ship can detect the unnavigable area, the drones should expand their formation to both sides, depending on the following situations:

[0198] Scenario 1: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with The formation reorganization parameters will be recalculated only when both sides of the ship's drones detect an unnavigable area or only one side's drones detect an unnavigable area.

[0199] Furthermore, when the detection range of the drone formation is At this time, the detection range is at its widest, and there is no need to regroup the formation;

[0200] Scenario 2: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with , Replace with The formation reorganization parameters will be recalculated only when both sides of the ship's drones detect an unnavigable area, or only one side's drones detect an unnavigable area. and auxiliary calculation parameters ;

[0201] Scenario 3: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with The formation reorganization parameters will be recalculated only when both sides of the ship's drones detect an unnavigable area or only one side's drones detect an unnavigable area.

[0202] Scenario 4: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with The formation reorganization parameters will be recalculated only when both sides of the ship's drones detect an unnavigable area or only one side's drones detect an unnavigable area.

[0203] When only one side of the ship's drones detects an unnavigable area, i.e. the drones cannot obtain the width of the navigable waters, the drone formation maintains its current formation until both sides of the ship's drones detect an unnavigable area or neither can detect an unnavigable area, at which point the distribution of drone mission points is calculated.

[0204] Step 2: Based on the distribution of UAV mission points, define the mathematical expression for each UAV mission point as follows:

[0205]

[0206] in, This is a state matrix for UAV mission points, representing the UAV mission points respectively. axis, axis, Axis coordinates; Represents a rotation matrix; Representing the relative positions of the UAV mission points to the ship mission points, this is the formation matrix; by changing... It can realize the reorganization of drone formations.

[0207] The above three scenarios relate to the formation reorganization parameters. and auxiliary calculation parameters The calculation can change the relative position matrix between the UAV mission point and the ship mission point, enabling the adaptive reorganization of ship / UAV formations in the navigation waters.

[0208] In a specific embodiment, using the ship's mission point and the UAV's mission point as the desired coordinates, and based on Stackelberg game theory, locally optimal motion strategies for the ship / UAV and the virtual ship / UAV are constructed respectively. The optimal motion strategy for the ship / UAV is then obtained based on these locally optimal strategies, so that the ship / UAV reaches the desired coordinates.

[0209] S31. Constructing locally optimal motion strategies for ships / UAVs based on Stackelberg game theory:

[0210] The performance metrics for the follower layer in the Stackelberg game between ships / drones and virtual ships / drones are as follows:

[0211]

[0212] in, This represents the performance metrics of the follower layer. Represents time, To account for the error between the ship / drone and the virtual ship / drone, For the ship / UAV state matrix, For virtual state matrix, These are the motion strategies employed by ships / drones and virtual ships / drones, respectively. Both are positive symmetric matrices, representing ships / drones and virtual ships / drones respectively. The weight it occupies in the middle;

[0213] According to the principles of differential game theory, it is possible to obtain minimum value This refers to the locally optimal motion strategy for ships / UAVs, therefore, constructing... The local optimal motion strategy for ships / UAVs with the minimum value is:

[0214]

[0215] in, for The minimum value, for The estimated value; The local optimal motion strategy for the ship / UAV is given by, where, These are the local optimal motion strategies for ships and drones, respectively. for The estimated value; where, They are respectively The estimated value; These are the weights and activation functions of a radial basis function neural network, respectively. They are respectively The critic and actor estimates; For ship / UAV kinematic control, the control parameter matrix is ​​provided.

[0216] S32. Based on Stackelberg game theory, construct the local optimal motion strategy for the virtual ship / machine:

[0217] The leadership performance metrics for designing a Stackelberg game between ships / drones and virtual ships / drones are:

[0218]

[0219] in, Represents leadership performance indicators; The error between the virtual ship / aircraft and the mission point; Both are positive symmetric matrices, representing virtual ships / aircraft and ships / drones respectively. The weight it occupies in the middle; The task matrix represents the desired formation, i.e., the desired coordinates of ships / UAVs;

[0220] Based on the principles of differential game theory, construct a system that... The local optimal motion strategy for the virtual ship / machine with the minimum value is:

[0221]

[0222] in, for The minimum value, Then it is The estimated value; The local optimal motion strategy for the virtual ship / machine. Its estimated value; These are the weights and activation functions of a radial basis function neural network, respectively. They are respectively The critic and actor estimates; This is the control parameter matrix for virtual ship / machine kinematic control.

[0223] S33. Obtain the optimal motion strategy for the ship / UAV based on the local optimal motion strategies of the ship / UAV and the virtual ship / UAV, including:

[0224] By combining the local optimal motion strategies of the ship / UAV and the virtual ship / UAV, the estimated value of the local optimal motion strategy of the ship / UAV is obtained, that is, the optimal motion strategy of the ship / UAV is:

[0225]

[0226] Construct an update law for the weight estimates of the neural network so that... Converging to ; Converging to ,make Converging to The update law is as follows:

[0227]

[0228] in, It is the identity matrix. All are positive constants, representing respectively Update rate; A positive constant represents the minimum update law.

[0229] In a specific embodiment, the scheme for constructing a ship / UAV position controller based on the optimal motion strategy, so that the actual positions of the ship and UAV converge to the corresponding task point coordinates, is as follows:

[0230] S41. Define the expression for the virtual position control through a first-order filter as follows:

[0231]

[0232] in, for The time constant of the first-order low-pass filter ; for The filtered signal;

[0233] S42. The expression for position dynamics error and its derivative is defined as follows:

[0234]

[0235]

[0236] S43. Based on the position dynamics error and its derivative, a ship / UAV position controller is constructed as follows:

[0237]

[0238] in, For the position control parameter matrix, Here, represents the weights and activation function of the positional radial basis function neural network, used to approximate the positional nonlinear matrix. ; for The estimated value; Position interference matrix The observed values ​​are shown below:

[0239]

[0240] in, For location interference observation parameters; For location interference auxiliary parameters; The update law is:

[0241]

[0242] In the formula, All are positive diagonal matrices, representing respectively The update rate and its minimum update law.

[0243] In a specific embodiment, a ship / UAV attitude master controller is constructed based on the ship's local optimal motion strategy and the UAV's actual position, so that the ship / UAV's attitude converges to the requirements of the optimal motion strategy; the ship / UAV attitude master controller includes an attitude virtual controller and a ship / UAV attitude controller; the scheme for controlling the ship and UAV to execute the optimal motion strategy according to the ship / UAV position controller and the ship / UAV attitude master controller to achieve coordinated control of the ship / UAV is as follows:

[0244] S51. Local Optimal Motion Strategy Based on Ship and drone position control input The ship / UAV reference attitude is calculated as follows:

[0245]

[0246] in, This is the ship / UAV reference attitude matrix, representing the ship's reference heading angle and the UAV's reference roll, pitch, and heading angles, respectively; where, This is the default value; Representing matrices respectively The first and second row elements; Represents the lift of the drone;

[0247] S52. Define the kinematic error of ship / UAV attitude as:

[0248]

[0249] A virtual attitude controller is constructed based on the kinematic errors of ship / UAV attitude:

[0250]

[0251] in, For attitude virtual controller; A positive symmetric matrix, representing the attitude virtual control parameter matrix;

[0252] S53. The attitude virtual controller is filtered using a first-order low-pass filter to obtain... ;

[0253]

[0254] In the formula, for The time constant of the first-order low-pass filter for The filtered signal;

[0255] The attitude dynamics error is defined as:

[0256]

[0257] A ship / UAV attitude controller is constructed based on attitude dynamics errors as follows:

[0258]

[0259] In the formula, This is the attitude control parameter matrix; These are the weights and activation functions of the attitude radial basis function neural network, used to approximate the position nonlinear matrix. ; for The estimated value; Attitude disturbance matrix The observed values ​​are shown below.

[0260]

[0261] In the formula, For attitude disturbance observation parameters; For attitude disturbance auxiliary parameters;

[0262] also, The update law can be expressed as

[0263]

[0264] In the formula, All are positive diagonal matrices, representing respectively The update rate and its minimum update law;

[0265] By controlling the ship / UAV position controller and the UAV attitude controller to execute the optimal motion strategy, the ship and UAV can achieve coordinated control.

[0266] To verify the effectiveness of the proposed ship / UAV game-theoretic optimization guidance and control algorithm in ice condition detection missions in narrow polar waterways, computer simulation experiments were conducted using MATLAB, and its robustness and accuracy were compared with existing control algorithms.

[0267] Example 1:

[0268] This embodiment is a numerical simulation experiment simulating interference in a polar marine environment. The narrow channel is flanked by two irregular ice floes, each 3000 m long. A 38 m long ship and four 0.486 kg rotary-wing UAVs are selected as the controlled objects. When the UAVs are at a flight altitude of 100 meters, their detection range radius is... Set waypoints as , , , , The initial state of the ship / drone is as follows: The initial attitude is The initial linear velocity is ;

[0269] The initial angular velocity is The initial state of the virtual ship / machine is as follows: The initial formation structure is as follows: , , , The initial state of the ship's mission point is as follows: The speed is always .

[0270] The results are as follows Figures 4-8 As shown:

[0271] Figure 4 The figures show the ship / UAV movement trajectories and UAV detection coverage results. Figure (a) is a two-dimensional planar view, and (b) is a three-dimensional spatial view. As can be seen from the figures, the ship / UAV cooperative system can navigate along narrow channels of waypoints. At the same time, the UAV can dynamically adjust its detection coverage formation around the ship based on the width of the detected navigable waters, avoiding repeated detection of non-navigable ice floes and improving the efficiency of ship / UAV ice perception.

[0272] Figure 5 The positional error of the ship / UAV is shown in Figure (a), where (a) represents the positional error of the ship / UAV along the path. x (a) Position error of axis motion; (b) Position error of ship / UAV along axis motion. y (c) is the position error of the axis motion; z Position error of the shaft movement; as shown in the figure. Each is a matrix The elements in rows 1, 2, 3, 4, and 5 represent the ship's movement along... x , y Axis and drone along x , y , z The position error of the shaft. As shown in the figure, using the control method of this invention, the position error of both the ship and the UAV can converge to near 0.

[0273] Figure 6 The figure illustrates the change in linear velocity of the UAV during flight. In the figure, (a) represents the change in linear velocity of the UAV along... x The linear velocity of the axis motion, (b) is the velocity of the UAV along the axis. y (c) is the linear velocity of the UAV along the axis; z The linear velocity of the axis of motion; as can be seen from the figure, the UAV can autonomously change its flight speed to achieve formation reorganization.

[0274] The formation reorganization process is as follows Figure 7 As shown, (a) represents the formation reorganization parameters, and (b) represents the auxiliary calculation parameters. When the formation changes, it means that the drone reconnaissance formation is being reorganized. If there are no changes, the drone detection formation will remain unchanged.

[0275] Figure 8 The figures show the observation results of ocean disturbances. Figure (a) shows the observation results of disturbances in the ship's forward direction, and (b) shows the observation results of disturbances in the ship's bow roll direction. These represent the forces exerted by ocean disturbances in the ship's forward direction and the moments in the ship's bow roll direction, respectively, represented by the gray dashed lines in the figure. They are respectively The observed values ​​are shown in black in the figure, which shows that the proposed algorithm can accurately observe the forces and moments caused by ocean disturbances.

[0276] Example 2:

[0277] This embodiment compares the present invention with algorithms in existing literature, namely adaptive backstepping control laws based on dynamic ocean current disturbance observations, to verify the superiority of the present invention in terms of disturbance compensation and control accuracy. In this embodiment, the initial state of the ship is as follows: The initial attitude is The initial velocity is The initial state of the ship's mission point is as follows: The initial attitude is The speed is The bow roll speed is

[0278]

[0279] Therefore, the ship's mission point path can be obtained. The ship's tracking of the mission point path is achieved using both the present invention and an adaptive backstepping control law based on dynamic ocean current disturbance observation. The path tracking control accuracy is compared, and the comparison results are as follows: Figures 9-10 As shown:

[0280] Figure 9 The results of the ship's path tracking control under two control algorithms show that the present invention can make the ship get closer to the ship's mission point path.

[0281] Figure 10 This is a schematic diagram of the path tracking control error results. For distance error, The error is the attitude error. Clearly, the control algorithm of this invention has smaller control error and higher control accuracy. Meanwhile, existing methods exhibit more severe, frequent, and significant chattering, meaning that the control algorithm of this invention has stronger robustness and anti-interference capabilities.

[0282] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A game-theoretic guidance and control method for ship-based unmanned aerial vehicles (UAVs) for waterway ice condition detection, characterized in that, include: S1: The Euler-Lagrange equations are used to construct a three-degree-of-freedom model of the ship and a six-degree-of-freedom nonlinear mathematical model of the UAV, which will be used as the control objects in the future. S2: Based on actual ship waypoints, design ideal ship mission points, including: Definition of the first The waypoints and their coordinates are as follows: The preceding and following waypoints and their coordinates are represented as follows: and , ; Define a first straight navigation segment, a second straight navigation segment, and a turning segment between three consecutive waypoints; define task points located in the two straight navigation segments and the two task points located in the turning segment. Case 1: If the current segment is a straight navigation segment, then the ship's mission points for the first and second straight navigation segments are obtained based on the waypoints. The expressions for the ship's mission points are as follows: in, The ship's mission points axis, Axis coordinates, heading angle, forward speed, and roll speed; definitions This is the state matrix of the ship's mission points; the initial state of the ship's mission points is set as follows: ; When the ship's mission point is located on the first straight segment of navigation, it is defined as follows: and for: When the ship's mission point is located on the second straight segment of navigation, it is defined as follows: and for: ； in, and These are the headings for the first and second straight sections of the straight route, respectively. Case 2: If the current segment is a turning segment, then define for: in, This represents the difference in heading between the second straight-line navigation segment and the first straight-line navigation segment. ; The turning radius is expressed as follows: in, and These are the maximum turning radius and the minimum turning radius, respectively. Based on the turning radius, the ship's mission point and waypoint for the straight navigation segment, the expression for the mission point of the turning segment is as follows: in, for and The coordinates of the mission points for the turning segments between them. for and The coordinates of the mission points for the turning segments between them; Based on the relative relationship between the drone's detection radius and the real-time water width, drone mission points are generated; S3: Using the ship's mission point and the UAV's mission point as the desired coordinates, based on Stackelberg game, construct the local optimal motion strategies for the ship / UAV and the virtual ship / UAV respectively, and obtain the optimal motion strategy for the ship / UAV based on the local optimal motion strategies of the ship / UAV and the virtual ship / UAV so that the ship / UAV can reach the desired coordinates. S4: Construct a ship / UAV position controller based on the optimal motion strategy to converge the actual positions of the ship and UAV to the corresponding task point coordinates; S5: Construct a ship / UAV attitude master controller based on the ship's local optimal motion strategy and the UAV's actual position, so that the ship / UAV's attitude converges to the requirements of the optimal motion strategy; the ship / UAV attitude master controller includes an attitude virtual controller and a ship / UAV attitude controller; control the ship and UAV to execute the optimal motion strategy according to the ship / UAV position controller and the ship / UAV attitude master controller, so as to realize the coordinated control of the ship / UAV.

2. The method for game-theoretic guidance and control of ship-based unmanned aerial vehicles (UAVs) for waterway ice condition detection according to claim 1, characterized in that, The Euler-Lagrange equations are used to construct a three-degree-of-freedom model for ships and a six-degree-of-freedom nonlinear mathematical model for unmanned aerial vehicles, including: The three-degree-of-freedom model of the ship and the six-degree-of-freedom nonlinear mathematical model of the UAV are shown below: in, and They are respectively ships and the The state matrix of each UAV, where each element represents the ship's position in a fixed coordinate system. axis, Coordinates on the axis and the drone in axis, shaft and Coordinates on the axis; The attitude matrix represents the ship's heading angle and the UAV's roll, pitch, and heading angles, respectively. This is a linear velocity matrix, representing the forward velocity of the ship and the velocity of the UAV along its path. axis, shaft and The speed of the shaft; Represents the ship's drift speed; This is an angular velocity matrix, representing the ship's bow rate and the UAV's roll, pitch, and bow rates, respectively. Let be the quality matrix, where, The mass of the ship in the forward direction, For the quality of the drone; Let be the moment of inertia matrix, representing the mass of the ship in the bow direction and the mass of the UAV along the direction of rotation. axis, axis, Moment of inertia of the shaft; The mass of the vessel in the lateral drift direction; The position control input matrix represents the ship's forward control input and the UAV's position control input. axis, axis, Control inputs on the axis; The attitude control input matrix represents the ship's yaw control input and the UAV's roll, pitch, and yaw control inputs, respectively. This is the gravitational acceleration matrix; This is a position interference matrix, representing the interference experienced by the ship in its forward direction and the interference experienced by the UAV in the following directions. axis, axis, Interference experienced on the axis; The attitude interference matrix represents the interference experienced by the ship in the bow direction and the interference experienced by the UAV in the roll, pitch, and bow directions, respectively. The position nonlinearity matrix represents the system nonlinear parameters of the ship in the forward direction and the UAV in the direction of travel, respectively. axis, axis, Nonlinear parameters of the system on the axis; For attitude nonlinear parameters, denoted as the system nonlinear parameters of the ship in the yaw direction and the system nonlinear parameters of the UAV in the heel, pitch, and yaw directions, respectively. For the system nonlinear parameters of the ship in the lateral drift direction; in, These respectively represent the drones in axis, axis, Nonlinear parameters in the axial, tilt, pitch, and yaw directions; These are the moment of inertia and rotational speed of the UAV rotor, respectively. These are the first, second, and third order parameters of the nonlinear system for the ship's forward direction, respectively. These are the first, second, and third order parameters of the nonlinear system in the lateral drift direction of the ship, respectively. These are the first, second, and third order parameters of the ship's bow roll direction nonlinear system, respectively.

3. The ship-based UAV game-theoretic guidance and control method for waterway ice condition detection according to claim 1, characterized in that, Based on the relative relationship between the UAV's detection radius and the real-time water width, UAV mission points are generated, including: Step 1: Determine the width of the navigable area Size: When both sides of the ship's drones detect unnavigable areas, i.e., areas of floating ice, the width of the navigable area is... The value can have the following possibilities: Scenario 1: When When designing the distribution formula for UAV mission points, the formula is: in, For formation reorganization parameters; R represents the altitude of the UAV. Detection radius at that time; Scenario 2: When When designing the distribution formula for UAV mission points, the formula is: in, To assist in calculating parameters, ; Scenario 3: When When designing the distribution formula for UAV mission points, the formula is: in, ; Scenario 4: When When designing the distribution formula for UAV mission points, the formula is: in, ; Scenario 5: When When designing the distribution formula for UAV mission points, the formula is: When neither of the drones on either side of the ship can detect the unnavigable area, the values ​​used to determine the detection range of the drone formation can fall into the following categories: Scenario 1: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with ; Scenario 2: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with , Replace with ; Scenario 3: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with ; Scenario 4: When the detection range of the drone formation is At that time, At that time, the distribution formula of UAV mission points Replace with ; When only one side of the ship's drones detects an unnavigable area, i.e. the drones cannot obtain the width of the navigable waters, the drone formation maintains its current formation until both sides of the ship's drones detect an unnavigable area or neither can detect an unnavigable area, at which point the distribution of drone mission points is calculated. Step 2: Based on the distribution of UAV mission points, define the mathematical expression for each UAV mission point as follows: in, This is a state matrix for UAV mission points, representing the UAV mission points respectively. axis, axis, Axis coordinates; Represents a rotation matrix; This represents the relative position of the UAV mission point to the ship mission point, forming a formation matrix.

4. The ship-based UAV game-theoretic guidance and control method for waterway ice condition detection according to claim 3, characterized in that, Using the ship's mission point and the UAV's mission point as the desired coordinates, and based on Stackelberg game theory, local optimal motion strategies for the ship / UAV and the virtual ship / UAV are constructed respectively, including: S31. Constructing locally optimal motion strategies for ships / UAVs based on Stackelberg game theory: The performance metrics for the follower layer in the Stackelberg game between ships / drones and virtual ships / drones are as follows: in, This represents the performance metrics of the follower layer. Represents time, To account for the error between the ship / drone and the virtual ship / drone, For the ship / UAV state matrix, For virtual state matrix, These are the motion strategies employed by ships / drones and virtual ships / drones, respectively. Both are positive symmetric matrices, representing ships / drones and virtual ships / drones respectively. The weight it occupies in the middle; Based on the principles of differential game theory, construct a system that... The local optimal motion strategy for ships / UAVs with the minimum value is: in, for The minimum value, for The estimated value; The local optimal motion strategy for the ship / UAV is given by, where, These are the local optimal motion strategies for ships and drones, respectively. for The estimated value; where, They are respectively The estimated value; These are the weights and activation functions of a radial basis function neural network, respectively. They are respectively The critic and actor estimates; For ship / UAV kinematic control, the control parameter matrix is ​​provided. S32. Based on Stackelberg game theory, construct the local optimal motion strategy for the virtual ship / machine: The leadership performance metrics for designing a Stackelberg game between ships / drones and virtual ships / drones are: in, Represents leadership performance indicators; The error between the virtual ship / aircraft and the mission point; Both are positive symmetric matrices, representing virtual ships / aircraft and ships / drones respectively. The weight it occupies in the middle; The task matrix represents the desired formation, i.e., the desired coordinates of ships / UAVs; Based on the principles of differential game theory, construct a system that... The local optimal motion strategy for the virtual ship / machine with the minimum value is: in, for The minimum value, Then it is The estimated value; The local optimal motion strategy for the virtual ship / machine. Its estimated value; These are the weights and activation functions of a radial basis function neural network, respectively. They are respectively The critic and actor estimates; This is the control parameter matrix for virtual ship / machine kinematic control.

5. The ship-based UAV game-theoretic guidance and control method for waterway ice condition detection according to claim 4, characterized in that, The optimal motion strategy for a ship / UAV is obtained based on the local optimal motion strategies of the ship / UAV and the virtual ship / UAV, including: By combining the local optimal motion strategies of the ship / UAV and the virtual ship / UAV, the estimated value of the local optimal motion strategy of the ship / UAV is obtained, that is, the optimal motion strategy of the ship / UAV is: Construct an update law for the weight estimates of the neural network so that... Converging to ; Converging to ,make Converging to The update law is as follows: in, It is the identity matrix. All are positive constants, representing respectively Update rate; A positive constant represents the minimum update law.

6. The ship-based UAV game-theoretic guidance and control method for waterway ice condition detection according to claim 5, characterized in that, Construct a ship / drone position controller based on the optimal motion strategy, including: S41. Define the expression for the virtual position control through a first-order filter as follows: in, for The time constant of the first-order low-pass filter ; for The filtered signal; S42. The expression for position dynamics error and its derivative is defined as follows: S43. Based on the position dynamics error and its derivative, a ship / UAV position controller is constructed as follows: in, For the position control parameter matrix, Here, represents the weights and activation function of the positional radial basis function neural network, used to approximate the positional nonlinear matrix. ; for The estimated value; Position interference matrix The observed values ​​are shown below: in, For location interference observation parameters; For location interference auxiliary parameters; The update law is: In the formula, All are positive diagonal matrices, representing respectively The update rate and its minimum update law.

7. The ship-based UAV game-theoretic guidance and control method for waterway ice condition detection according to claim 6, characterized in that, A ship / UAV attitude controller is constructed based on the ship's local optimal motion strategy and the UAV's actual position, including: S51. Local Optimal Motion Strategy Based on Ship and drone position control input The reference attitude of the ship / UAV is calculated as follows: in, This is the ship / UAV reference attitude matrix, representing the ship's reference heading angle and the UAV's reference roll, pitch, and heading angles, respectively; where, This is the default value; Representing matrices respectively The first and second row elements; The lift of the drone; S52. Define the kinematic error of ship / UAV attitude as: A virtual attitude controller is constructed based on the kinematic errors of ship / UAV attitude: in, For attitude virtual controller; A positive symmetric matrix, representing the attitude virtual control parameter matrix; S53. The attitude virtual controller is filtered using a first-order low-pass filter to obtain... ; In the formula, for The time constant of the first-order low-pass filter for The filtered signal; The attitude dynamics error is defined as: A ship / UAV attitude controller is constructed based on attitude dynamics errors as follows: In the formula, This is the attitude control parameter matrix; These are the weights and activation functions of the attitude radial basis function neural network, used to approximate the position nonlinear matrix. ; for The estimated value; Attitude disturbance matrix The observed values ​​are shown below. In the formula, For attitude disturbance observation parameters; For attitude disturbance auxiliary parameters; also, The update law can be expressed as In the formula, All are positive diagonal matrices, representing respectively The update rate and its minimum update law.

Images