Aircraft trajectory analysis planning method meeting multiple physical constraints

Abstract

The invention discloses an aircraft trajectory analysis planning method meeting multiple physical constraints, which comprises the following steps: in a three-dimensional space, according to a position relationship between an aircraft and a fixed target, constructing a kinematics equation for describing a motion state of the aircraft relative to the target; the relative kinematics equation is converted into a differential equation with the relative distance as an independent variable through equation transformation; respectively constructing polynomial functions of a front angle component relative to a relative distance in a pitch plane and a yaw plane, obtaining a front angle profile with only one to-be-set parameter based on a boundary condition, and exporting a control law that a terminal instruction is not divergent; and based on the proximity angle constraint and in combination with a kinematics equation, performing approximate solution and real-time updating on unknown parameters through a series expansion method, and finally obtaining a control law with an analysis form. According to the method, dependence on model linearization, constant speed hypothesis and a parameter numerical optimization method is avoided, and the trajectory planning requirement with the approach angle constraint is met.

Description

Technical Field

[0001] The present invention belongs to the field of aircraft trajectory planning and control, and in particular relates to an aircraft trajectory analytical planning method that satisfies multiple physical constraints. Background Art

[0002] Generally speaking, the main task of aircraft trajectory planning is to design a reasonable path to guide the aircraft to the predetermined target point, usually with collision avoidance and cost-saving as flight constraints. This type of task has a single objective, simple design, and relatively mature methods. However, planning methods that only consider precise intersections have certain limitations. For example, in practical tasks such as civil monitoring and inspection, logistics distribution, and disaster investigation, aircraft often need to approach the target area at different angles to achieve wider coverage, more accurate delivery, or more efficient observation. If only traditional planning methods are used, the optimal arrival effect may not be achieved, resulting in deviations from expectations and affecting the overall quality of the mission. Currently, an effective improvement is to use a trajectory planning method with approach angle constraints. This method can ensure that the aircraft reaches the target location at the expected angle and enables multiple aircraft to work together, effectively improving the efficiency of mission completion.

[0003] At the same time, for most aircraft, terminal control command divergence is prone to occur during actual trajectory planning. This not only causes the flight path to deviate from the ideal trajectory but also seriously affects flight stability and safety. Furthermore, when planning trajectories in three-dimensional space, the strong coupling between the dimensions of the equations of motion makes it difficult to directly extend relatively mature two-dimensional trajectory planning methods. This has become a major issue that needs to be addressed in the current trajectory planning field. Existing methods often require switching strategies, constant velocity assumptions, or linearization of the system model, and involve extensive parameter tuning, which greatly limits their practicality and applicability.

[0004] Therefore, studying a vehicle trajectory analytical planning method that meets multiple physical constraints is of great significance for enhancing system applicability, improving mission execution reliability, and simplifying the planning process. Summary of the Invention

[0005] To address the aforementioned technical issues, the present invention proposes an analytical method for aircraft trajectory planning that satisfies multiple physical constraints. This method utilizes approach angles and boundary conditions to determine unknown parameters, thereby obtaining an analytically accurate lead angle profile and corresponding control instructions. Compared to existing methods, the analytical method employed in the present invention eliminates the need for model linearization, constant velocity assumptions, or complex profile parameter design and adjustment. It can simultaneously meet the requirements for bounded approach angles and terminal control instructions, effectively avoiding the conservative limitations of existing methods while improving their applicability and reliability to actual missions.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for analytic planning of aircraft trajectories satisfying multiple physical constraints comprises the following steps:

[0008] S1: In three-dimensional space, based on the positional relationship between the aircraft and the fixed target, construct the kinematic equation that describes the motion state of the aircraft relative to the target;

[0009] S2: By transforming between equations, the relative kinematic equation is transformed into a differential equation with relative distance as the independent variable;

[0010] S3: Construct polynomial functions of the lead angle components with respect to relative distance in the pitch plane and the yaw plane respectively. Based on the boundary conditions, a lead angle profile with only one parameter to be tuned is obtained, and a control law with no divergence in the final state is derived.

[0011] S4: Based on the approach angle constraint and combined with the kinematic equations, the unknown parameters are approximately solved and updated in real time through the series expansion method, and finally a control law with an analytical form is obtained.

[0012] Beneficial effects:

[0013] (1) The analytical control law designed in this invention can not only realize the approach angle constraint, but also ensure the terminal command divergence.

[0014] (2) The present invention adopts an analytical method based on the reshaping of the pre-angle profile, which does not require linearization of the model, does not have any profile parameters that need to be adjusted, and does not rely on the constant velocity assumption. It has the characteristics of simple design method, strong applicability, and high reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A flow chart of the aircraft trajectory analytical planning method satisfying multiple physical constraints of the present invention;

[0016] Figure 2 It is a schematic diagram of the intersection between the aircraft and the stationary target point in three-dimensional space;

[0017] Figure 3 Schematic diagram of simulation of the trajectory analysis planning method of the present invention under the first set of approach angle constraints;

[0018] Among them, (a)-(f) represent the aircraft flight trajectory, aircraft speed change trend, line of sight pitch angle component change curve, line of sight azimuth angle component change curve, aircraft pitch plane normal acceleration change curve, and aircraft yaw plane normal acceleration change trend in scenario 1, respectively. DETAILED DESCRIPTION

[0019] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0020] The present invention provides an analytical aircraft trajectory planning method that satisfies multiple physical constraints. First, in three-dimensional space, based on the positional relationship between the aircraft and a fixed target, a kinematic equation describing the motion state of the aircraft relative to the target is constructed. Second, by transforming between equations, the relative kinematic equation is converted into a differential equation with relative distance as the independent variable. Then, a polynomial function of the lead angle component with respect to the relative distance is constructed in the pitch plane and the yaw plane, respectively. Based on the boundary conditions, a lead angle profile with only one parameter to be adjusted is obtained, and a control law is derived in which the terminal command does not diverge. Finally, based on the approach angle constraint and in combination with the kinematic equation, the unknown parameters are approximately solved and updated in real time by the series expansion method to obtain a control law with an analytical form. The present invention adopts a trajectory shaping method based on the lead angle-relative distance, avoiding the reliance on model linearization, constant velocity assumption, and parameter numerical optimization method, and meeting the requirements of trajectory planning with approach angle constraints.

[0021] Specifically, if Figure 1 As shown, an aircraft trajectory analytical planning method that satisfies multiple physical constraints according to an embodiment of the present invention includes:

[0022] S1: If Figure 2 As shown, Figure 2 middle and Represent the aircraft and target respectively; is the relative distance between the aircraft and the stationary target point; LOS stands for line of sight; is the flight speed of the aircraft; , are the pitch and yaw lead angle components of the aircraft; , are the pitch and azimuth components of the aircraft's line of sight angle relative to the target point; , , They are the inertial coordinate system, the body coordinate system, and the line of sight coordinate system. According to the kinematic and dynamic relationship between the aircraft and the stationary target in three-dimensional space, the mathematical model of the aircraft's motion relative to the stationary target point in three-dimensional space is:

[0023] (1)

[0024] (2)

[0025] (3)

[0026] (4)

[0027] (5)

[0028] (6)

[0029] in, is the relative distance between the aircraft and the stationary target point; is the flight speed of the aircraft; , are the pitch and yaw lead angle components of the aircraft; , are the pitch and azimuth components of the aircraft's line of sight angle relative to the target point; , is the leading angular component angular rate of the aircraft; , is the angular velocity of the line of sight component of the aircraft relative to the target point; , is the normal acceleration of the aircraft in the pitch and yaw planes, which also requires the design of control laws; is the rate of change of velocity; is the acceleration due to gravity; The thrust generated for the aircraft; is the aerodynamic resistance, which can be expressed by the formula calculate; is the drag coefficient; is the atmospheric density; is the reference area; The mass of the aircraft.

[0030] S2: By transforming between equations, the relative kinematic equations are transformed into differential equations with relative distance as the independent variable, including:

[0031] Dividing the left and right sides of equations (2) to (5) by the two sides of equation (1) respectively, we can obtain:

[0032] (7)

[0033] (8)

[0034] (9)

[0035] (10)

[0036] S3: Construct polynomial functions of the lead angle components with respect to relative distance in the pitch plane and the yaw plane, respectively. Based on the boundary conditions, a lead angle profile with only one parameter to be tuned is obtained, and a control law with no final state divergence is derived, including:

[0037] Construct a cubic polynomial function of the lead angle component with respect to the relative distance in the pitch plane and the yaw plane respectively:

[0038] (11)

[0039] (12)

[0040] As the desired lead angle profile, where is the initial relative distance; , is the desired lead angle component; , , , , is the parameter to be designed. Taking the first derivative, we get:

[0041] (13)

[0042] (14)

[0043] in, , They are , Relative distance The first-order derivative of . The boundary conditions that the desired lead angle profile needs to meet at the initial moment are:

[0044] (15)

[0045] Through formula (15), we can get:

[0046] (16)

[0047] The boundary conditions that the desired lead angle profile needs to meet at the initial moment are:

[0048] (17)

[0049] in, 、 are the pitch and yaw lead angle components of the aircraft at the initial moment. Through formula (17), we can get:

[0050] (18)

[0051] Substituting Equations (16) and (18) into Equations (11) to (14), we can obtain the lead angle profile with only one parameter to be adjusted:

[0052] (19)

[0053] (20)

[0054] (twenty one)

[0055] (twenty two)

[0056] Combining Equation (21), Equation (22), Equation (9) and Equation (10), we can obtain the control law:

[0057] (twenty three)

[0058] Combined with L'Hôpital's rule, we can get a non-divergent terminal instruction:

[0059] (twenty four)

[0060] in, and are the normal terminal commands for the pitch and yaw planes.

[0061] S4: Based on the approach angle constraint and combined with the kinematic equations, the unknown parameters are approximately solved and updated in real time through the series expansion method, ultimately obtaining a control law with an analytical form, including:

[0062] Compare Equation (7) with Equation (8) Integrating, we get:

[0063] (25)

[0064] (26)

[0065] in, and are the pitch and azimuth components of the initial line of sight between the aircraft and the target; is the integration variable.

[0066] Applying the small lead angle assumption, we can obtain the following equation (25):

[0067] (27)

[0068] when When , we can get:

[0069] (28)

[0070] in, Indicates the pitch component of the approach angle.

[0071] Applying the small lead angle assumption and Taylor series expansion, we can obtain the following equation (26):

[0072] (29)

[0073] when When , we can get:

[0074] (30)

[0075] in, represents the azimuth component of the approach angle. , ,in and For the desired pitch and azimuth components of the approach angle, we can obtain:

[0076] (31)

[0077] (32)

[0078] Considering that any current moment can be regarded as the initial moment of the subsequent trajectory, replacing the initial values ​​in Equations (31) and (32) with real-time values, we can obtain:

[0079] (33)

[0080] (34)

[0081] It should be understood that all variables with dots on them in the present invention are derivatives of the variables, unless the derivative of the variable has actual physical meaning.

[0082] Combining Equations (21)-(23), (31) and (32), we can obtain the control law in analytical form.

[0083] The following example uses the rendezvous task between an aircraft and a stationary target point to verify the effectiveness of the three-dimensional trajectory planning method proposed in this invention. The aircraft speed is 250 m / s, the initial position of the aircraft is (0, 0, 5) km, the initial position of the target is (5, 5, 0) km, and the maximum acceleration limit of the aircraft is 60 The initial leading angles of the aircraft are selected as 20° for pitch angle component and -40° for yaw angle component, the aircraft mass is selected as 90 kg, and the aircraft reference area is selected as 0.5 The other simulation parameters are set as follows:

[0084] (35)

[0085] in, Represents the flight altitude; Represents Mach number.

[0086] The trajectory planning simulation results for this rendezvous mission are as follows: Figure 3 As shown in FIG, the simulation scenario selects the pitch angle component of the ideal approach angle as -20°, and the azimuth angle components are -20°, 20°, 60°, and 100° respectively. Figure 3 (a)-(f) represent the aircraft flight trajectory, aircraft speed change trend, line of sight pitch angle component change curve, line of sight azimuth component change curve, aircraft pitch plane normal acceleration change curve, aircraft yaw plane normal acceleration change trend in this scenario. Figure 3 It can be seen that the method proposed in the present invention can effectively and accurately intersect with the stationary target point under the desired approach angle constraint, and ensures that the aircraft control instructions converge to a finite value.

[0087] In summary, the trajectory planning method proposed in the present invention effectively realizes the requirements of approach angle and finite terminal command constraints without relying on model linearization and constant velocity assumptions, and there are no profile parameters that need to be adjusted.

Claims

1. A method for aircraft trajectory analytical planning that satisfies multiple physical constraints, characterized in that: The following steps are involved: S1: In three-dimensional space, based on the positional relationship between the aircraft and the fixed target, construct the kinematic equation that describes the motion state of the aircraft relative to the target; S2: By transforming between equations, the kinematic equation of the aircraft's relative motion state to the target is transformed into a differential equation with relative distance as the independent variable; S3: Construct polynomial functions of the lead angle components with respect to relative distance in the pitch plane and the yaw plane, respectively. Based on the boundary conditions, a lead angle profile with only one parameter to be tuned is obtained, and a control law is derived to ensure that the terminal command does not diverge. S4: Based on the approach angle constraint and combined with the kinematic equations, the unknown parameters are approximately solved and updated in real time through the series expansion method, and finally a control law with an analytical form is obtained.

2. The method for analyzing and planning aircraft trajectories satisfying multiple physical constraints according to claim 1, wherein: In S1, the kinematic equation of the aircraft relative to the stationary target point in three-dimensional space is: （1） （2） （3） （4） （5） （6） in, is the relative distance between the aircraft and the stationary target point; is the flight speed of the aircraft; , are the pitch and yaw lead angle components of the aircraft; , are the pitch and azimuth components of the aircraft's line of sight angle relative to the target point; , is the leading angular component angular rate of the aircraft; , is the angular velocity of the line of sight component of the aircraft relative to the target point; , is the normal acceleration of the aircraft in the pitch and yaw planes, which also requires the design of control laws; is the rate of change of velocity; is the acceleration due to gravity; The thrust generated for the aircraft; is the aerodynamic resistance, through the formula calculate; is the drag coefficient; is the atmospheric density; is the reference area; The mass of the aircraft.

3. The method for aircraft trajectory analytical planning satisfying multiple physical constraints according to claim 2, characterized in that: In S2, the kinematic and dynamic equations are transformed into differential equations with relative distance as the independent variable: （7） （8） （9） （10）。 4. The method for analytic planning of aircraft trajectories satisfying multiple physical constraints according to claim 1, wherein: The S3 includes: Construct a cubic polynomial function of the lead angle component with respect to the relative distance in the pitch plane and the yaw plane respectively: （11） （12） As the desired lead angle profile, where is the initial relative distance; , is the desired lead angle component; , , , , Parameters that need to be designed.

5. The method for aircraft trajectory analytical planning satisfying multiple physical constraints according to claim 4, characterized in that: Compare Equation (11) and Equation (12) to the relative distance Taking the first derivative, we get: （13） （14） in, , They are , Relative distance The first derivative of .

6. The method for aircraft trajectory analytical planning satisfying multiple physical constraints according to claim 5, characterized in that: The boundary conditions that the desired lead angle profile needs to meet at the initial moment are: （15） Through formula (15), we can get: （16） The boundary conditions that the desired lead angle profile needs to meet at the initial moment are: （17） in, 、 are the pitch and yaw lead angle components of the aircraft at the initial moment; Through formula (17), we can get: （18） Substituting Equations (16) and (18) into Equations (11) to (14), we obtain the lead angle profile with only one parameter to be adjusted: （19） （20） （21） （22） Combining Equation (21), Equation (22), Equation (9) and Equation (10), we get the control law: （23）。 7. The method for analytic planning of aircraft trajectories satisfying multiple physical constraints according to claim 6, characterized in that: Combined with L'Hôpital's rule, we get the terminal instruction that does not diverge: （24） in, and are the normal terminal commands for the pitch and yaw planes.

8. The method for aircraft trajectory analytical planning satisfying multiple physical constraints as claimed in claim 3, characterized in that: The S4 includes: Compare Equation (7) with Equation (8) Integrating, we get: （25） （26） in, and are the pitch and azimuth components of the initial line of sight between the aircraft and the target; is the integration variable.

9. The method for aircraft trajectory analytical planning satisfying multiple physical constraints according to claim 8, characterized in that: Applying the small lead angle assumption, we can obtain the following equation (25): （27） when When , we get: （28） in, represents the pitch component of the approach angle; Applying the small lead angle assumption and Taylor series expansion, we can obtain the following equation (26): （29） when When , we get: （30） in, Represents the azimuth component of the approach angle.

10. The method for aircraft trajectory analytical planning satisfying multiple physical constraints according to claim 9, characterized in that: By order , ,in and For the desired pitch and azimuth components of the approach angle, we have: （31） （32） Combining Equations (21)-(23), (31) and (32), we obtain the control law in analytical form.

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