Guiding and controlling method for net collision recovery of ship-borne fixed-wing unmanned aerial vehicle

Abstract

The invention discloses a guidance and control method for net collision recovery of a ship-borne fixed-wing unmanned aerial vehicle, and belongs to the field of flight control of aircrafts. According to the method, a recovery net image shot by a ship-borne unmanned aerial vehicle camera is utilized, related variables are calculated, a mathematical model of relative movement under sight coordinates is established, a guide instruction of unmanned aerial vehicle net collision recovery is deduced based on the Lyapunov stability principle, and high-precision net collision recovery is achieved through flight control.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft flight control, and in particular to a guidance and control method for recovering a shipborne fixed-wing unmanned aerial vehicle (UAV) when it crashes into a net. Background Art

[0002] With the rapid development of drone technology, the application of shipborne drones is becoming more and more extensive. However, the safe and accurate recovery of drones, especially in harsh marine environments, has become one of the problems that restrict their widespread application. Existing recovery technologies such as GPS navigation and radar guidance are often plagued by problems such as signal obstruction and insufficient positioning accuracy. The guidance and control methods used are often affected by factors such as the starting position and orientation, requiring track generation and smoothing, and the guidance and control logic is complex. Summary of the invention

[0003] The present invention provides a guidance and control method for the recovery of a shipborne fixed-wing UAV after it hits a net. Based on visual positioning information, a tracking guidance method is adopted to design the guidance and control of the UAV, so as to achieve high-precision and safe recovery of the fixed-wing UAV after it hits a net in a shipborne environment.

[0004] The embodiment of the present invention provides a method for guiding and controlling the recovery of a shipborne fixed-wing UAV when it hits a net. The recovery net is installed on the ship and moves synchronously with the navigation of the ship. The method includes the following steps:

[0005] Step 1: obtaining the line of sight information of the shipborne UAV relative to the recovery net according to the recovery net image taken by the shipborne UAV, and obtaining the flight information of the shipborne UAV and the navigation information of the ship;

[0006] Step 2, using line of sight information, flight information and navigation information to establish a mathematical model of the line of sight state quantity of the UAV's net-collision recovery movement;

[0007] Step 3: Based on the expression of the sight line elevation angle in the sight line state quantity mathematical model, a Lyapunov function is constructed, and according to the Lyapunov stability requirement, the longitudinal pitch angle rate guidance instruction of the carrier-based UAV is solved;

[0008] Step 4: Based on the expression of the line of sight azimuth in the line of sight state quantity mathematical model, a Lyapunov function is constructed, and according to the Lyapunov stability requirement, the lateral roll angle guidance instruction of the carrier-based UAV is solved;

[0009] Step 5: Based on the line of sight distance expression in the line of sight state quantity mathematical model, a Lyapunov function is constructed, and according to the Lyapunov stability requirement, the speed control instruction of the carrier-based UAV is solved;

[0010] Step 6: Design the flight control law of the shipborne UAV, construct the rudder control, and achieve tracking of guidance and control instructions.

[0011] Optionally, in one embodiment of the present invention, in step 1, obtaining the sight line information of the shipborne drone relative to the recovery net according to the recovery net image taken by the shipborne drone includes: the sight line height angle λ of the shipborne drone relative to the center of the recovery net lon and the line of sight azimuth λ lat , and the line-of-sight distance ρ between the shipborne UAV and the recovery network;

[0012] The flight information of the carrier-based UAV includes the pitch angle θ, the heading angle ψ A , track inclination angle γ and current flight speed V A ;

[0013] The navigation information of the ship includes: the navigation speed V S and heading angle ψ S .

[0014] Optionally, in one embodiment of the present invention, step 2 includes:

[0015] The rate of change of the line of sight distance ρ in the inertial coordinate system is the ship velocity vector V S With the speed vector V of the shipborne drone A The difference is:

[0016]

[0017] In the inertial coordinate system, the velocity vector V of the carrier-based UAV is A With the ship velocity vector V S The three-axis component expressions are:

[0018]

[0019] Among them, γ is the track inclination angle of the carrier-based UAV, ψ A is the heading angle of the shipborne UAV, ψ S is the heading angle of the ship; the rate of change of the line of sight distance ρ in the line of sight coordinate system is expressed as:

[0020]

[0021] in, R y , R z They are the transformation matrices from the inertial coordinate system to the line of sight coordinate system, defined as:

[0022]

[0023] Among them, θ is the pitch angle of the shipborne UAV, λ lon is the sight angle of the shipborne UAV relative to the center of the recovery network, λ lat is the sight angle of the shipborne UAV relative to the center of the recovery network, and the above formula is expanded to:

[0024]

[0025] The rate of change of the sight vector in the sight coordinate system is expressed as follows:

[0026]

[0027] Get the rate of change of sight distance Line of sight azimuth change rate and the rate of change of sight height angle The expression is:

[0028]

[0029]

[0030] Optionally, in one embodiment of the present invention, step 3 includes:

[0031] Construct the Lyapunov function of the sight line elevation angle:

[0032]

[0033] According to Lyapunov's stability requirements, let its derivative The pitch rate guidance command of the carrier-based UAV is obtained as follows:

[0034]

[0035] Among them, the longitudinal control gain coefficient K lon >0.

[0036] Optionally, in one embodiment of the present invention, step 4 includes:

[0037] Construct the Lyapunov function for the line of sight azimuth:

[0038]

[0039] According to Lyapunov's stability requirements, let its derivative The yaw rate guidance instruction of the carrier-based UAV is obtained as follows:

[0040]

[0041] Among them, the lateral control gain coefficient K is selected lat >0;

[0042] When the shipborne drone makes a coordinated turn in the side channel:

[0043]

[0044] Among them, g is the acceleration of gravity, φ is the roll angle of the shipborne UAV;

[0045] The lateral roll angle guidance instructions for the shipborne UAV are:

[0046]

[0047] Optionally, in one embodiment of the present invention, step 5 includes:

[0048] Construct the Lyapunov function for line of sight distance:

[0049]

[0050] According to the requirements of Lyapunov stability, let its derivative The speed control command of the carrier-based UAV is obtained as follows:

[0051]

[0052] Among them, V C is the set speed of the drone hitting the net, V C >0.

[0053] Optionally, in one embodiment of the present invention, step 6 includes:

[0054] Designing a flight control law for a shipborne UAV to respectively track the longitudinal pitch angle rate guidance command of the shipborne UAV, the lateral roll angle guidance command of the shipborne UAV and the speed control command of the shipborne UAV;

[0055] The longitudinal elevator control law of the shipborne UAV is:

[0056]

[0057] Among them, δ e is the deflection of the elevator of the shipborne UAV, is the elevator control gain coefficient of the shipborne UAV, is the pitch rate of the shipborne UAV, Provides pitch rate guidance instructions for shipborne UAVs;

[0058] The lateral aileron control law of the shipborne UAV is:

[0059]

[0060] Among them, δa is the deflection of the aileron rudder of the shipborne UAV, K φ , K φ is the aileron control gain coefficient of the shipborne UAV, φ c It is the lateral roll angle guidance instruction for the shipborne UAV. is the roll angular rate of the shipborne UAV;

[0061] The throttle control law of the shipborne UAV is:

[0062]

[0063] Among them, δ T is the throttle opening of the carrier-based UAV, K V , K VI is the throttle control gain coefficient of the shipborne UAV, δ T0 is the base throttle opening, Provides speed control instructions for shipborne UAVs;

[0064] The control law of the rudder of the shipborne UAV is:

[0065] δ r =K r r+K β β

[0066] Among them, δ r is the rudder deflection of the shipborne UAV, r is the body axis yaw rate of the shipborne UAV, β is the sideslip angle of the shipborne UAV, K r , K β is the rudder control gain coefficient of the shipborne UAV.

[0067] The guidance and control method for recovering a shipborne fixed-wing UAV after hitting a net in an embodiment of the present invention goes deep into the field of aircraft flight control technology and ensures the safety and efficiency of the UAV recovery process through a highly intelligent method. The present invention uses real-time line of sight information, such as the relative position, speed, and attitude between the UAV and the recovery net, to design a set of precise guidance and control algorithms. Through this algorithm, the UAV can autonomously adjust its flight trajectory in a complex marine environment, accurately track and lock the recovery net target, and achieve autonomous recovery after hitting a net without human intervention.

[0068] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0070] Figure 1This is a flow chart of a method for guiding and controlling a shipborne fixed-wing UAV to recover a network according to an embodiment of the present invention;

[0071] Figure 2 Schematic diagram of the longitudinal motion relationship of the shipborne UAV hitting the net and recovering in an embodiment of the present invention;

[0072] Figure 3 Schematic diagram of the lateral motion relationship of the shipborne UAV hitting the net and recovering in an embodiment of the present invention;

[0073] Figure 4 1 is a structural diagram of a shipborne UAV net-collision recovery guidance and control system in an embodiment of the present invention. DETAILED DESCRIPTION

[0074] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0075] Figure 1 The present invention provides a flow chart of a method for guiding and controlling a shipborne fixed-wing UAV during net collision recovery according to an embodiment of the present invention.

[0076] like Figure 1 As shown, the guidance and control method for recovering a shipborne fixed-wing UAV after it hits a net includes the following steps:

[0077] Step 1: According to the recovery net image taken by the shipborne UAV, the line of sight information of the shipborne UAV relative to the recovery net is obtained, and the flight information of the shipborne UAV and the navigation information of the ship are obtained.

[0078] In an embodiment of the present invention, the recovery net is installed on the ship and moves synchronously with the navigation of the ship. An optical marker that is easy to track is set on the recovery net. The ship-borne drone is located at the rear of the ship, and its fuselage is equipped with a high-resolution camera, and the lens of the camera is aimed directly in front of the axis of the drone fuselage.

[0079] The shipborne UAV enters the recovery phase and uses its onboard camera to capture images of the recovery net. After image processing, the height angle λ of the shipborne UAV relative to the center of the recovery net is obtained. lon and the line of sight azimuth λ lat , and the line-of-sight distance ρ between the shipborne UAV and the recovery network.

[0080] The sensor system is used to obtain the UAV’s shipborne flight attitude and state parameters in real time, including the pitch angle θ and heading angle ψ of the shipborne UAV. A , track inclination angle γ and current flight speed V A; At the same time, the shipboard sensor system obtains the ship's navigation speed V S and heading angle ψ S .

[0081] Step 2: Use line of sight information, flight information and navigation information to establish a mathematical model of the line of sight state quantity of the UAV's net-collision recovery movement.

[0082] According to the relationship between the rate of change of the sight distance vector and the speed vector of the drone and the recovery net, the embodiment of the present invention derives and establishes a sight state quantity mathematical model that meets the requirements of net recovery. Step 2 includes:

[0083] The rate of change of the line of sight distance ρ in the inertial coordinate system is the ship velocity vector V S With the speed vector V of the shipborne drone A The difference is:

[0084]

[0085] In the inertial coordinate system, the velocity vector V of the carrier-based UAV is A With the ship velocity vector V S The three-axis component expressions are:

[0086]

[0087] Among them, γ is the track inclination angle of the carrier-based UAV, ψ A is the heading angle of the shipborne UAV, ψ S is the heading angle of the ship; the rate of change of the line of sight distance ρ in the line of sight coordinate system is expressed as:

[0088]

[0089] in, R y , R z They are the transformation matrices from the inertial coordinate system to the line of sight coordinate system, defined as:

[0090]

[0091] Among them, θ is the pitch angle of the shipborne UAV, λ lon is the sight angle of the shipborne UAV relative to the center of the recovery network, λ lat is the line of sight azimuth of the shipborne UAV relative to the center of the recovery net. Since the camera is installed on the shipborne UAV, its coordinate system is consistent with the body coordinates, so the attitude angle of the camera is consistent with the attitude angle of the UAV.

[0092] Expand further The expression of the three-axis components is:

[0093]

[0094] Depend on Figure 2 , Figure 3 The schematic diagram of the relationship between the longitudinal and lateral motions of the UAV net recovery is shown in the figure. The three-axis components of the line of sight vector change rate in the line of sight coordinate system are expressed as:

[0095]

[0096] In summary, the rate of change of sight distance is Line of sight azimuth change rate and the rate of change of sight height angle The expression is:

[0097]

[0098] Step 3: Based on the expression of the line of sight elevation angle in the line of sight state mathematical model, construct the Lyapunov function, and solve the longitudinal pitch angle rate guidance command of the shipborne UAV according to the Lyapunov stability requirements.

[0099] In an embodiment of the present invention, step 3 includes:

[0100] Construct the Lyapunov function of the sight line elevation angle:

[0101]

[0102] According to Lyapunov's stability requirements, when W1>0, if its derivative The system is asymptotically stable and the tracking error is zero. During the recovery process of the UAV hitting the net, the vertical sight angle tends to zero, indicating that the UAV is aligned with the recovery net in the vertical channel. Taking the derivative of W1, we can get:

[0103]

[0104] Let its derivative The pitch rate guidance command of the carrier-based UAV is obtained as follows:

[0105]

[0106] Among them, the longitudinal control gain coefficient K lon >0.

[0107] In order to avoid the situation where the UAV’s line of sight distance ρ gradually decreases when approaching the recovery network, resulting in a large pitch rate command, it is set that when ρ is less than 0.2 meters, K lon Take 0.01.

[0108] Step 4: Based on the expression of the line of sight azimuth in the line of sight state quantity mathematical model, construct the Lyapunov function, and solve the lateral roll angle guidance instruction of the shipborne UAV according to the Lyapunov stability requirements.

[0109] In an embodiment of the present invention, step 4 includes:

[0110] Construct the Lyapunov function for the line of sight azimuth:

[0111]

[0112] According to Lyapunov's stability requirements, when W2>0, if its derivative The system is asymptotically stable and the tracking error is zero. That is, during the recovery process, the lateral line of sight azimuth tends to zero, indicating that the UAV is aligned with the recovery net in the lateral channel. Taking the derivative of W2, we can get:

[0113]

[0114] Let its derivative W2 < 0, and the yaw rate guidance instruction of the carrier-based UAV is obtained as:

[0115]

[0116] Among them, the lateral control gain coefficient K is selected lat >0;

[0117] During the flight of the UAV, the lateral channel should meet the requirements of coordinated turning. When the shipborne UAV makes a coordinated turn in the lateral channel:

[0118]

[0119] Among them, g is the acceleration of gravity, φ is the roll angle of the shipborne UAV;

[0120] Therefore, the lateral roll angle guidance instruction of the shipborne UAV is:

[0121]

[0122] In order to avoid the situation where the UAV approaches the recovery net and the line of sight distance ρ gradually decreases, resulting in a large roll angle command, it is set that when ρ is less than 0.2m, K lat Take 0.01.

[0123] Step 5: Based on the line-of-sight distance expression in the line-of-sight state quantity mathematical model, construct the Lyapunov function, and solve the speed control command of the shipborne UAV according to the Lyapunov stability requirements.

[0124] In an embodiment of the present invention, step 5 includes:

[0125] Construct the Lyapunov function for line of sight distance:

[0126]

[0127] According to the requirements of Lyapunov stability, when W3>0, its derivative The system gradually stabilizes and the tracking error approaches zero. During the recovery process, the distance between the drone and the recovery net gradually decreases, and eventually the drone hits the net at a certain speed. Taking the derivative of W3, we get:

[0128]

[0129] Let its derivative The speed control command of the carrier-based UAV is obtained as follows:

[0130]

[0131] Among them, V C is the set speed of the drone hitting the net, V C >0.

[0132] Step 6: Design the flight control law of the shipborne UAV, construct the rudder control, and achieve tracking of guidance and control instructions.

[0133] according to Figure 4 The structure diagram of the shipborne UAV recovery guidance and control system. The guidance instructions obtained by steps 2, 3 and 4 are input into the UAV flight control system. The UAV flight control law is designed to track the longitudinal pitch angle rate guidance instructions of the shipborne UAV, the lateral roll angle guidance instructions of the shipborne UAV and the speed control instructions of the shipborne UAV.

[0134] In an embodiment of the present invention, step 6 includes:

[0135] The longitudinal elevator control law of the shipborne UAV is:

[0136]

[0137] Among them, δ e is the deflection of the elevator of the shipborne UAV, is the elevator control gain coefficient of the shipborne UAV, is the pitch rate of the shipborne UAV, Provides pitch rate guidance instructions for shipborne UAVs;

[0138] The lateral aileron control law of the shipborne UAV is:

[0139]

[0140] Among them, δ a is the deflection of the aileron rudder of the shipborne UAV, Kφ , K φ is the aileron control gain coefficient of the shipborne UAV, φ c It is the lateral roll angle guidance instruction for the shipborne UAV. is the roll angular rate of the shipborne UAV;

[0141] The throttle control law of the shipborne UAV is:

[0142]

[0143] Among them, δ T is the throttle opening of the carrier-based UAV, K V , K VI is the throttle control gain coefficient of the shipborne UAV, δ T0 is the base throttle opening, Provides speed control instructions for shipborne UAVs;

[0144] The control law of the rudder of the shipborne UAV is:

[0145] δ r =K r r+K β β

[0146] Among them, δ r is the rudder deflection of the shipborne UAV, r is the body axis yaw rate of the shipborne UAV, β is the sideslip angle of the shipborne UAV, K r , K β is the rudder control gain coefficient of the shipborne UAV.

[0147] According to the guidance and control method for the recovery of a shipborne fixed-wing UAV after it hits a net, an image of the recovery net taken by a camera of the shipborne UAV is used to calculate relevant variables and establish a mathematical model of relative motion in line-of-sight coordinates. Based on the Lyapunov stability principle, guidance instructions for the recovery of the UAV after it hits a net are derived, and high-precision recovery after it hits a net is achieved through flight control.

[0148] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0149] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "N" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0150] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present invention belong.

Claims

1. A method for guiding and controlling the recovery of a shipborne fixed-wing UAV after it hits a net. The recovery net is installed on the ship and moves synchronously with the navigation of the ship. The method is characterized in that: The method comprises the following steps: Step 1: obtaining the line of sight information of the shipborne UAV relative to the recovery net according to the recovery net image taken by the shipborne UAV, and obtaining the flight information of the shipborne UAV and the navigation information of the ship; Step 2, using line of sight information, flight information and navigation information to establish a mathematical model of the line of sight state quantity of the UAV's net-collision recovery movement; Step 3: Based on the expression of the sight line elevation angle in the sight line state quantity mathematical model, a Lyapunov function is constructed, and according to the Lyapunov stability requirement, the longitudinal pitch angle rate guidance instruction of the carrier-based UAV is solved; Step 4: Based on the expression of the line of sight azimuth in the line of sight state quantity mathematical model, a Lyapunov function is constructed, and according to the Lyapunov stability requirement, the lateral roll angle guidance instruction of the carrier-based UAV is solved; Step 5: Based on the line of sight distance expression in the line of sight state quantity mathematical model, a Lyapunov function is constructed, and according to the Lyapunov stability requirement, the speed control instruction of the carrier-based UAV is solved; Step 6: Design the flight control law of the shipborne UAV, construct the rudder control, and achieve tracking of guidance and control instructions.

2. The method according to claim 1, characterized in that In step 1, the sight line information of the shipborne drone relative to the recovery net is obtained according to the recovery net image taken by the shipborne drone, including: the sight line height angle λ of the shipborne drone relative to the center of the recovery net lon and the line of sight azimuth λ lat , and the line-of-sight distance ρ between the shipborne UAV and the recovery network; The flight information of the carrier-based UAV includes the pitch angle θ, the heading angle ψ A , track inclination angle γ and current flight speed V A ; The navigation information of the ship includes: the navigation speed V S and heading angle ψ S .

3. The method according to claim 1, characterized in that Step 2 includes: The rate of change of the line of sight distance ρ in the inertial coordinate system is the ship velocity vector V S With the speed vector V of the shipborne drone A The difference is: In the inertial coordinate system, the velocity vector V of the carrier-based UAV is A With the ship velocity vector V S The three-axis component expressions are: Among them, γ is the track inclination angle of the carrier-based UAV, ψ A is the heading angle of the shipborne UAV, ψ S is the heading angle of the ship; The rate of change of the sight distance ρ in the sight coordinate system is expressed as: in, R y , R z They are the transformation matrices from the inertial coordinate system to the line of sight coordinate system, defined as: Among them, θ is the pitch angle of the shipborne UAV, λ lon is the sight angle of the shipborne UAV relative to the center of the recovery network, λ lat is the sight angle of the shipborne UAV relative to the center of the recovery network, and the above formula is expanded to: The rate of change of the sight vector in the sight coordinate system is expressed as follows: Get the rate of change of sight distance Line of sight azimuth change rate and the rate of change of sight height angle The expression is:

4. The method according to claim 3, characterized in that Step 3 includes: Construct the Lyapunov function of the sight line elevation angle: According to Lyapunov's stability requirements, let its derivative The pitch rate guidance command of the carrier-based UAV is obtained as follows: Among them, the longitudinal control gain coefficient K lon >0.

5. The method according to claim 3, characterized in that: Step 4 includes: Construct the Lyapunov function for the line of sight azimuth: According to Lyapunov's stability requirements, let its derivative The yaw rate guidance instruction of the carrier-based UAV is obtained as follows: Among them, the lateral control gain coefficient K is selected lat >0; When the shipborne drone makes a coordinated turn in the side channel: Among them, g is the acceleration of gravity, φ is the roll angle of the shipborne UAV; The lateral roll angle guidance instructions for the shipborne UAV are:

6. The method according to claim 3, characterized in that Step 5 includes: Construct the Lyapunov function for line-of-sight distance: According to the requirements of Lyapunov stability, let its derivative The speed control command of the carrier-based UAV is obtained as follows: Among them, V C is the set speed of the drone hitting the net, V C >0.

7. The method according to claim 3, characterized in that Step 6 includes: Designing a flight control law for a shipborne UAV to respectively track the longitudinal pitch angle rate guidance command of the shipborne UAV, the lateral roll angle guidance command of the shipborne UAV and the speed control command of the shipborne UAV; The longitudinal elevator control law of the shipborne UAV is: Among them, δ e is the deflection of the elevator of the shipborne UAV, is the elevator control gain coefficient of the shipborne UAV, is the pitch rate of the shipborne UAV, Provides pitch rate guidance instructions for shipborne UAVs; The lateral aileron control law of the shipborne UAV is: Among them, δ a is the deflection of the aileron rudder of the shipborne UAV, K φ , is the aileron control gain coefficient of the shipborne UAV, φ c It is the lateral roll angle guidance instruction for the shipborne UAV. is the roll angular rate of the shipborne UAV; The throttle control law of the shipborne UAV is: Among them, δ T is the throttle opening of the carrier-based UAV, K V , K VI is the throttle control gain coefficient of the shipborne UAV, δ T0 is the base throttle opening, Provides speed control instructions for shipborne UAVs; The control law of the rudder of the shipborne UAV is: d r =K r r+K β b Among them, δ r is the rudder deflection of the shipborne UAV, r is the body axis yaw rate of the shipborne UAV, β is the sideslip angle of the shipborne UAV, K r , K β is the rudder control gain coefficient of the shipborne UAV.

Images