Steering control method and system of electric vertical lifting aircraft

Abstract

The invention relates to a steering control method of an electric vertical lifting aircraft, which comprises the following steps: acquiring a steering starting point and a steering ending point, and generating an expected steering curve according to three-dimensional coordinates of the steering starting point and the steering ending point; according to the expected steering curve, the position of the stress change point on the expected steering curve is determined, and the expected steering curve is divided into a first stage and a second stage according to the position; a steering wheel is used for controlling the running direction of the aircraft, when the aircraft is in the first stage, the stress of the aircraft in the lifting direction is constant, and when the aircraft is in the second stage, the aircraft adjusts the power of front and rear motors according to the steering direction, so that the flight attitude of the aircraft is changed; when the aircraft reaches the steering end point, the power of the four motors is adjusted to be consistent, and the aircraft completes steering. The steering area of the aircraft is divided into two stages, different modes are adopted for flight according to different stages, the whole steering stage does not decelerate or even accelerate, the aircraft steers smoothly, and the drifting effect similar to automobile turning is achieved.

Description

Technical Field

[0001] This invention relates to the field of aircraft technology, specifically to a steering control method and system for an electric vertical takeoff and landing aircraft. Background Technology

[0002] EVTOL (Electric Vertical Take-Off and Landing) aircraft are civilian general-purpose low-altitude aircraft designed for airspace from 0 to 3000 meters. These motor-driven aircraft possess vertical take-off and landing capabilities, allowing them to operate without a runway. The motors are powered by electric energy sources, including batteries and fuel cells. They offer numerous advantages such as low cost, zero emissions, low noise, fewer components, safety backups for core components, and a lower accident rate compared to traditional aircraft.

[0003] However, existing manned electric vertical takeoff and landing aircraft use levers for turning, which have short and non-linear control strokes, resulting in unsmooth turning. Furthermore, because attitude and direction are controlled by intermittent adjustments, the aircraft may even tilt outwards due to inertia when moving forward and turning rapidly, leading to a poor passenger experience and the risk of being thrown out of the aircraft, thus reducing pilot safety. Summary of the Invention

[0004] The purpose of this invention is to provide a steering control method for an electric vertical takeoff and landing aircraft to solve the problems in the prior art.

[0005] A first aspect of the present invention provides a steering control method for an electric vertical takeoff and landing (EVTOL) aircraft, comprising: S1. Obtain the steering start point and steering end point, and generate the expected smooth steering curve based on the three-dimensional coordinates of the steering start point and the steering end point; S2. Based on the expected steering curve, determine the position of the force change point on the expected steering curve, and divide the expected steering curve into a first stage and a second stage based on the position. S3. The steering wheel is used to control the direction of the aircraft's movement. When the aircraft is in the first stage, the aircraft's altitude and force in the climbing direction are constant. When the aircraft is in the second stage, the power of the four motors is adjusted according to the turning direction, so that the aircraft's flight attitude changes. S4. When the aircraft reaches the turning termination point, the power of the four motors is adjusted to be consistent, and the aircraft completes the turning.

[0006] In one possible implementation, determining the position of the force change point on the expected steering curve based on the expected steering curve includes: Obtain the slope of each point on the expected curve. When the slope reaches a preset slope threshold, the point is the point of force change.

[0007] In one possible implementation, the aircraft is a quadcopter, and the flight attitude changes include: Reduce the output power of the two motors on the inner side of the fuselage in the yaw direction, and increase the output power of the two motors on the outer side of the fuselage in the yaw direction, so that the aircraft fuselage can roll inward at an angle.

[0008] In one possible implementation, the yaw angle during the aircraft's turn is obtained, and the output power of each motor is adjusted in real time based on the yaw angle so that the aircraft flies according to the expected turn curve.

[0009] In one possible implementation, the two motors at the head of the machine rotate in opposite directions, and the two motors at the tail of the machine rotate in opposite directions.

[0010] In one possible implementation, determining the point of force change further includes: Real-time monitoring of the aircraft's dynamic parameters during the turning process, including lateral acceleration and pitch angle change rate; The location of the point of force change is determined when the following conditions are met simultaneously: The real-time slope of the expected curve reaches the preset slope threshold. The absolute value of the lateral acceleration is greater than a preset acceleration threshold and the duration exceeds a first time threshold; The yaw angle change rate is greater than a preset angle change rate threshold.

[0011] A second aspect of the present invention provides a steering control system for an electric vertical takeoff and landing (EVTOL) aircraft, the steering control system being used to execute the aforementioned steering control method, comprising: A steering wheel is used to control the direction of movement of an aircraft. Throttle and brake are used to control the speed of the aircraft; The first motor is located on the right side of the aircraft's nose; the second motor is located on the right side of the aircraft's tail; the third motor is located on the left side of the aircraft's nose; and the fourth motor is located on the left side of the aircraft's tail. A PID controller is used to analyze the flight trajectory of the aircraft and issue flight commands to the steering wheel based on the flight trajectory. Sensors are used to collect real-time attitude and position information of aircraft.

[0012] In one possible implementation, the steering wheel includes a disc body and up / down buttons, the up / down buttons being disposed on the disc body.

[0013] In one possible implementation, the yaw angle and roll angle generated during the flight of the aircraft controlled by the steering wheel are input as expected values ​​into the PID controller. The PID controller calculates and outputs control commands based on the expected values ​​through the PID control differential equation, and adjusts the power distribution of each motor according to the control commands to achieve a smooth arc of flight trajectory.

[0014] In one possible implementation, during the aircraft's turn, the relationship between the aircraft's speed, turning radius, and roll angle is determined by the formula: v = (g * tanθ) n *r) 1 / 2 In the formula, v is the speed of the aircraft, r is the turning radius, and θ is the turning radius. n The roll angle is set to θ; when the speed v is greater than the preset threshold and the turn is completed, the roll angle θ is increased. n This reduces the turning radius r (i.e., completing the turn with a smaller radius); when the speed v is less than or equal to a preset threshold, the roll angle θ n The linear decrease results in an increase in the turning radius r (i.e., completing the turn with a larger radius).

[0015] Compared with the prior art, the beneficial effects of the present invention are: 1. By dividing the aircraft's turning into two stages and using different methods for different stages, the aircraft's turning trajectory curve is smooth, the nose is consistent with the flight direction and maintains the inside turning angle, achieving a drifting effect similar to that of a car turning very safely. 2. Replacing the original lever control with a three-dimensional steering wheel can improve the accuracy and range of the aircraft's rotation direction during the turning process and increase the aircraft's control safety. Attached Figure Description

[0016] Figure 1 A turning trajectory for an existing electric vertical takeoff and landing aircraft; Figure 2 This is an alternative turning trajectory for existing electric vertical takeoff and landing aircraft. Figure 3 This is a flowchart illustrating the steering control method of the electric vertical take-off and landing aircraft of the present invention. Figure 4 This is a schematic diagram of the flight state during the turning process of the aircraft of the present invention; Figure 5 This is a schematic diagram showing the working states of each motor in this invention; Figure 6 This is a schematic diagram of the steering control system of the electric vertical takeoff and landing aircraft in this invention; Figure 7 This is a schematic diagram of the yaw angle during the turning process of the aircraft of the present invention; Figure 8This is a schematic diagram of the roll angle during the turning process of the aircraft of the present invention; Figure 9 This is a schematic diagram of the control principle of the PID controller in this invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0018] It should be noted that the serial numbers assigned to the components in the embodiments of the present invention, such as "first" and "second", are only used to distinguish the described objects and have no sequential or technical meaning.

[0019] When existing electric vertical takeoff and landing (EVTOL) aircraft make a turn (a complete 90° turn), they typically exhibit two states. The first is, as... Figure 1 As shown, if the aircraft accelerates forward with a pitch angle and makes a sharp turn during flight, the aircraft's flight attitude and trajectory are analyzed as follows (the aircraft is at a fixed altitude of 15 meters. During the flight, it flies past position A with its trajectory attitude perpendicular to the x-axis and flies to position C with its trajectory attitude perpendicular to the y-axis). Its flight trajectory is an irregular trajectory, the turning process is not smooth, and it cannot accelerate, which affects the flight experience.

[0020] The second type, such as Figure 2 As shown, if the aircraft changes its roll angle too early or too late during a turn, it will cause the aircraft's flight trajectory to become irregular. When it reaches position C, it may even need to decelerate and adjust its attitude to pass through position C perpendicular to the y-axis.

[0021] Based on this, the present invention provides a steering control method for an electric vertical takeoff and landing (EVTOL) aircraft, so that the trajectory of the aircraft during the steering process is a smooth curve, and it can accelerate during the steering. The following is in conjunction with... Figures 3-9 The steering control method of the vertical take-off and landing aircraft of the present invention is described.

[0022] A steering control method for an electric vertical takeoff and landing (EVTOL) aircraft includes: S1. Obtain the steering start point and steering end point, and generate the expected smooth steering curve based on the three-dimensional coordinates of the steering start point and the steering end point; The expected steering curve can be referenced from the steering drift curve of a car. A large number of car steering curves are input as a training set into a machine learning model, such as a deep learning network (GAN), to generate the required three-dimensional curve for the aircraft's steering from the input two-dimensional car steering curves. Through multiple training iterations, the expected steering curve for the aircraft can be obtained. When the aircraft steers according to the expected curve, it can achieve an effect similar to the inward-leaning drift of a sports car, resulting in a superior driving experience.

[0023] S2. Based on the expected steering curve, determine the position of the force change point on the expected steering curve, and divide the expected steering curve into a first stage and a second stage based on the position. Differentiating the curve at each point yields the slope of that point. When the slope reaches a preset slope threshold, that point is the point of force change. Figure 4 As shown in the figure, point A is the point that reaches the preset slope threshold. When determining the preset slope threshold, the aforementioned machine learning model can be used to analyze the trajectory of the expected curve. When drifting is required, the slope of this point is the slope threshold.

[0024] S3. Use the steering wheel to control the direction of the aircraft's movement. When the aircraft is in the first stage, the force on the aircraft in the direction of ascent and descent is constant. In this stage, the nose and tail of the aircraft remain on the same plane. Since this stage is the initial stage of turning and the inertia is small, the aircraft will not tail-swing due to inertia. Therefore, the aircraft can maintain a greater turning speed by keeping the force on the aircraft in the direction of ascent and descent constant. When the aircraft is in the second stage, the power of the four motors is adjusted according to the direction of turn, which changes the flight attitude of the aircraft. In this stage, the aircraft's turn begins to be affected by inertia and the tail begins to drift. In order to maintain the balance of the aircraft, it is necessary to adjust the attitude of the nose and tail to ensure that the aircraft can turn smoothly. S4. When the aircraft reaches the turning termination point, the power of the four motors is adjusted to be consistent, and the aircraft completes the turning.

[0025] To implement the aforementioned control method, this patent also provides a corresponding steering control system, such as... Figure 6 As shown, the steering control system includes: A steering wheel is used to control the direction of movement of an aircraft; the steering wheel includes a disc body and up and down buttons, the up and down buttons being located on the disc body.

[0026] Throttle and brake are used to control the speed of the aircraft; A PID controller is used to analyze the flight trajectory of the aircraft and issue flight commands to the steering wheel based on the flight trajectory. Sensors are used to collect real-time attitude and position information of the aircraft. The MPU6000 sensor can be used as an example.

[0027] The steering wheel is the core component of this patent. This patent uses a four-channel, three-dimensional steering wheel to replace the traditional control stick for controlling the aircraft's flight. Normally, rotating the steering wheel allows different quadcopter blades to work together to produce the desired nose-turn direction for the pilot, and originally, nose-turning didn't change the aircraft's trajectory. However, by incorporating inward tilting channels into the steering wheel, the aircraft is prevented from excessively tilting outwards due to inertia, thus avoiding an unsafe experience. What was once a simple horizontal, stationary rotation of the steering wheel becomes a more dynamic experience. By pressing the accelerator and following the steering wheel's direction, the aircraft moves forward, and when cornering, it propels the nose-turning force while simultaneously accelerating and tilting inwards with the steering wheel's rotation. This creates a more responsive, drifting experience during cornering.

[0028] Turn the steering wheel left: The aircraft turns left and tilts to the left simultaneously; Direction to the right: The aircraft turns right and tilts to the right simultaneously; Press the up button on the steering wheel: The aircraft ascends; Press the down arrow key on the steering wheel: The aircraft descends; Press the accelerator: The aircraft moves forward / accelerates; Applying the brakes: The aircraft decelerates / stops / reverses; The steering wheel also supports automatic and manual modes to adjust the aircraft's trajectory.

[0029] In this patent, such as Figure 5 As shown, the aircraft is a quadcopter, meaning it has four motors, each driving a propeller for flight. The four motors are numbered sequentially: motor 3 is located on the left side of the nose, motor 1 on the right side of the nose, motor 4 on the left side of the tail, and motor 2 on the right side of the tail. To facilitate control of the aircraft's steering, motor 1's PWM (Pulse Width Modulation) rotates clockwise, motor 2's PWM rotates counter-clockwise, motor 3's PWM rotates counter-clockwise, and motor 4's PWM rotates clockwise.

[0030] The forces acting on the aircraft during flight are explained below. The force required to steer the aircraft to turn left or right is defined as F. a(x) The force that causes the aircraft to fly left or right is denoted as F. b(x) The force that is forward and backward is denoted as F. c(x)， The upward and downward force is denoted as F. z(x) For a quadcopter, the forces acting on the four axes differ depending on the flight maneuver performed. Here, 'x' represents the number of the different motors.

[0031] Left turn control F a2 + F a3 >F a1 +F a4 ; Right turn control F a1 + F a4 >F a2 +F a3 ; Left flight control F b1 + F b2 >F b3 +F b4 ; Right flight control F b3 + F b4 >F b1 +F b2 ; Forward control F c2 + F c4 >F c1 +F c3 ; Backward control F c2 + F c4 <F c1 +F c3 ; Ascend Control F z1 +F z2 +F z3 +F z4 >G (aircraft gravity); Descending control F z1 +F z2 +F z3 +F z4 <G (aircraft gravity).

[0032] The following explains the forces acting on the propellers of each motor when the steering wheel is operated. Regardless of whether the steering wheel is turned left or right, or the accelerator or brake is pressed, the forces acting on the four propellers are as follows: F1 = F a1 + F b1 + F c1 + F z1 ; F2= F a2 + F b2 + F c2 + F z2 ; F3 = F a3 + F b3 + F c3 + F z3 ; F4 = Fa4 + F b4 + F c4 + F z4 ; refer to Figure 4 The steering control process of the aircraft is explained. The first stage is from point O to point A. During this stage, the forces acting on the aircraft do not change, and the aircraft flies in a straight line. When it reaches point A, the forces change. That is, point A in the diagram is the initial point of force change. During the process from position A to point C via point B, the force F in the ascending / descending direction changes. z No change, the forward and backward forces F c It can remain constant without acceleration or deceleration, while the change is produced by steering wheel control, generating the yaw angle F. a Force control, plus F b The force control for left-hand flight (the effect of tilt angle). The greater the force on the left-hand flight control, the greater the tilt angle. The F-axis during cornering is adjusted based on actual experimental data. b The continuous control parameters are determined by the circuitry.

[0033] For the point A where the force changes, the following method can be used for calibration and confirmation: First, after the system initially determines point A based on the slope threshold, it actively fine-tunes the power of each motor (e.g., increases the tail power by 5%). If the yaw rate of change dψ / dt of the aircraft increases significantly at this time (e.g., ≥20%), then the point is initially confirmed as a candidate point A.

[0034] Then, the lateral acceleration *a* during the turning process is acquired using the accelerometer onboard the aircraft. It is determined whether the |a| at candidate point C is lower than a preset acceleration threshold and whether the duration exceeds a first preset time (e.g., Δt > 0.2 s). Then, the roll angle change rate *dβ / dt* is calculated using gyroscope data. If the change rate of *dβ / dt* at candidate point B is greater than a preset change rate threshold, for example, ≥ 15... ∘ If the force changes at a point ( / s), then that point is taken as point C, where the force changes.

[0035] The aircraft flies along the Y-axis, and the steering wheel rotates within the range of [-90°, 90°]. The aircraft's rotation of the steering wheel causes a linear change in the potentiometer's voltage, which in turn causes the aircraft to output PWM signals to F. a2 + F a3 >F a1 +F a4 However, it also drives the auxiliary potentiometer, causing the aircraft to output F via PWM. b1 + F b2 >F b3 +F b4For example, a steering wheel angle change of 0 to 90 degrees corresponds to a linear tilt of the aircraft along the X-axis within a range of 0 to 30 degrees. The steering wheel rotation angle and the aircraft tilt angle have a linear relationship. The X-axis and Y-axis represent the horizontal plane in which the aircraft turns, while the Z-axis represents the direction of ascent and descent of the aircraft.

[0036] To make the aircraft turn left while simultaneously accelerating and drifting to the left, the tail pitch angle needs to be raised. This requires increasing the PWM2 / 4 of the two tail motors and decreasing the PWM3 / 1 of the two nose motors; simultaneously, increasing the PWM1 / 2 on the right and decreasing the PWM3 / 4 on the left; and also superimposing an increase in yaw PWM2 / 3 and a decrease in PWM1 / 4. After these effects are superimposed (not simply superimposed, but obtained through numerical feedback from the MPU6000 gyroscope and quaternion calculations to obtain the necessary PWM output data for each motor), in addition to completing the above trajectory, due to the left-flying F... b The action overcomes a small amount of inertia, thus providing an excellent and safe drifting experience.

[0037] When using a three-dimensional steering wheel to control the steering of an aircraft, PID controller parameters can be used.

[0038] The following describes the PID control of the three-dimensional steering wheel to ensure that the aircraft maintains a certain stability during the turning process. Figure 4 The curve shown is used for illustration.

[0039] Combination Figure 7 and Figure 8 The aircraft's yaw angle α changed from 0 to 90 degrees, completing the attitude adjustment, and the nose direction was perfectly aligned with the flight trajectory. For example, during the aircraft's flight along the target curve, the aircraft speed remained constant, and the yaw angle α changed between time t and time t-1. t and α t-1 They are the same. The velocity v remains constant, and the yaw angle θ... n If the flight radius r remains constant, then the centripetal force F n =mv 2 / r will generate a fixed centripetal force F n At this point, the aircraft's attitude is adjusted to produce a roll angle θ. n To maintain balance at this angle, the resultant force F of the four propellers... h =F1+F2+F3+F4, the angle between the force and the centripetal force is 90°-θ n F h The angle between the direction of gravity and the direction of gravity is θ n Centripetal force F n =m×g×tanθ n Gravity F z =mg, and F n = mv2 / r,m×g×tanθ n = mv 2 / r, g is 9.8, v is obtained 2 =9.8 × tanθ n ×r. The higher the speed, the greater the required yaw angle and the larger the required roll angle to achieve the minimum turning radius; conversely, at lower speeds, a smaller yaw angle is needed to achieve the same minimum turning radius. Using a hybrid control mode of steering wheel yaw and roll angles effectively meets the requirements for safe high-speed turns. When the aircraft is required to complete a 90-degree yaw angle at a high forward speed (while maintaining flight along the target curve), the roll angle θ needs to be increased to minimize the turning radius r. n The maximum set value is 30 degrees. When the aircraft completes this 90-degree yaw at a low speed (while maintaining flight along the target curve), the aircraft rolls linearly as the fuselage slowly rotates at a smaller yaw angle. The speed threshold for which to turn can be changed depending on factors such as aircraft mass.

[0040] according to Figure 9 The working principle of PID is illustrated below. The PID control process is explained as follows: The yaw angle and roll angle of the steering wheel are used as the given desired value n(t) as the outer loop input of the cascade PID dual-loop control, entering the standard cascade PID flow, and passing through the standard PID control differential equation: The PWM signals for each motor are calculated. In the formula, y(t) is the system output, n(t) is the desired value, and e(t) is the control input: e(t) = n(t) - y(t). u(t) is the control output, K p T is the proportionality coefficient. i Let T be the integration time constant. d is the differential time constant.

[0041] In the above algorithm, the change in aircraft angle is usually taken as a value in the range of 0 to 1000 in the flight control program, and the corresponding steering wheel travel of 180 degrees to the left and right is set. The program uses such a wide range of values ​​in combination with long-travel steering wheel control to make the mixed control of yaw angle and roll angle more linear, and the flight trajectory and flight attitude better.

[0042] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is used as an example. In practical applications, the above functions can be assigned to different functional modules, sub-modules, and units as needed, that is, the internal structure of the system can be divided into different functional units or modules to complete all or part of the functions described above.

[0043] 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 of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A steering control method for an electric vertical takeoff and landing aircraft, characterized in that, include: S1. Obtain the steering start point and steering end point, and generate the expected smooth steering curve based on the three-dimensional coordinates of the steering start point and the steering end point; S2. Based on the expected steering curve, determine the position of the force change point on the expected steering curve, and divide the expected steering curve into a first stage and a second stage based on the position. S3. The steering wheel is used to control the direction of the aircraft's movement. When the aircraft is in the first stage, the force on the aircraft in the direction of ascent and descent is constant. When the aircraft is in the second stage, the power of the four motors is adjusted according to the direction of turning, so that the flight attitude of the aircraft changes. S4. When the aircraft reaches the turning termination point, the power of the four motors is adjusted to be consistent, and the aircraft completes the turning.

2. The steering control method for an electric vertical takeoff and landing aircraft according to claim 1, characterized in that, Determining the position of the force change point on the expected steering curve based on the expected steering curve includes: Obtain the slope of each point on the expected curve. When the slope reaches a preset slope threshold, the point is the point of force change.

3. The steering control method for an electric vertical takeoff and landing aircraft according to claim 1, characterized in that, The aircraft is a quadcopter, and the changes in flight attitude include: Reduce the output power of the two motors on the inside of the steering wheel and increase the output power of the two motors on the outside of the steering wheel to make the aircraft roll inward by an angle.

4. The steering control method for an electric vertical takeoff and landing aircraft according to claim 3, characterized in that, Also includes: The yaw angle during the aircraft's turn is obtained, and the output power of each motor is adjusted in real time based on the yaw angle so that the aircraft flies according to the expected turn curve.

5. The steering control method for an electric vertical takeoff and landing aircraft according to claim 4, characterized in that, The two motors at the head of the machine rotate in opposite directions, and the two motors at the tail of the machine rotate in opposite directions.

6. The steering control method for an electric vertical takeoff and landing aircraft according to claim 5, characterized in that, The determination of the point of force change also includes: Real-time monitoring of the aircraft's dynamic parameters during the turning process, including lateral acceleration and pitch angle change rate; The location of the point of force change is determined when the following conditions are met simultaneously: The real-time slope of the expected curve reaches the preset slope threshold. The absolute value of the lateral acceleration is greater than a preset acceleration threshold and the duration exceeds a first time threshold; The yaw angle change rate is greater than a preset angle change rate threshold.

7. A steering control system for an electric vertical takeoff and landing (EVTOL) aircraft, the steering control system being used to execute the steering control method of any one of claims 1-6, comprising: A steering wheel is used to control the direction of movement of an aircraft. Throttle and brake are used to control the speed of the aircraft; The first motor is located on the right side of the aircraft's nose; the second motor is located on the right side of the aircraft's tail; the third motor is located on the left side of the aircraft's nose; and the fourth motor is located on the right side of the aircraft's tail. A PID controller is used to analyze the flight trajectory of the aircraft and issue flight commands to the steering wheel based on the flight trajectory. Sensors are used to collect real-time attitude and position information of aircraft.

8. The steering control system of the electric vertical takeoff and landing aircraft according to claim 7, characterized in that, The yaw and roll angles generated during the flight of the aircraft controlled by the steering wheel are input as expected values ​​into the PID controller. The PID controller calculates and outputs control commands based on the expected values ​​through the PID control differential equation. According to the control commands, the power distribution of each motor is adjusted to achieve a smooth arc of flight trajectory.

9. The steering control system of the electric vertical takeoff and landing aircraft according to claim 8, characterized in that, During an aircraft turn, the relationship between the aircraft's speed, turning radius, and roll angle is established using the formula: v = (g * tanθ) n *r) 1 / 2 In the formula, v is the speed of the aircraft, r is the turning radius, and θ is the turning radius. n The roll angle is set to θ; when the speed v is greater than the preset threshold and the turn is completed, the roll angle θ is increased. n This reduces the turning radius r; when the speed v is less than or equal to a preset threshold, the roll angle θ... n The linear decrease causes the turning radius r to increase.

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