Aircraft trajectory planning method considering terminal time and track deviation angle constraints

Abstract

The present invention discloses an aircraft trajectory planning method that considers terminal time and track angle constraints. Related products are further provided. In this method, the flight state time series and control input time series are iteratively updated based on the current flight state time series, the current bank angle command time series, the terminal time constraint, and the terminal track angle constraint. If the degree of proximity between two adjacent flight state time series meets the set requirements, the iteration terminates and the latest flight state time series and the latest control input time series are output. Otherwise, the next round of update operations is performed. The iterative operation is to calculate the following optimization problem: #imgabs0#; #imgabs1#.

Description

Technical Field

[0001] The present invention relates to an aircraft trajectory planning method and related products taking into account terminal time and track deviation angle constraints. Background Art

[0002] Trajectory planning methods based on optimal control theory are gaining increasing attention because their planned trajectories can meet certain optimality requirements. These methods formulate the trajectory generation problem as an optimal control problem and employ indirect and direct methods based on the Pontryagin minimum principle or the calculus of variations to solve it. The direct method, also known as the direct collocation method, essentially transforms the continuous optimal control problem into a discrete nonlinear optimization problem using various parameter discretization methods. Techniques such as sequential quadratic programming or interior point methods are then used to solve the optimal trajectory that meets performance requirements. Currently, the pseudospectral method is the most widely used parameter discretization method for solving continuous optimal control problems and is increasingly being applied to trajectory planning for high-speed aircraft. For example, segmented trajectory planning that considers no-fly zone constraints and waypoint constraints to address emergencies has been used. The feasibility of the algorithm has been verified using classical objective functions such as maximum longitudinal range, maximum lateral range, and minimum track angle change.

[0003] However, existing trajectory planning methods for high-speed aircraft have several challenges. These include sensitivity to initial guesses of the solution, and the highly nonlinear nature of the problem, which can lead to unstable solution times and even failure. Furthermore, limited research exists on tasks that simultaneously consider both terminal time coordination and angular coordination constraints.

[0004] Chinese invention patent CN113805599B proposes a multi-constraint trajectory rapid planning method based on a parameterized control profile: by designing a parameterized angle of attack control profile, the angle of attack and time are used as parameters to be adjusted to adjust the terminal speed of the aircraft; the control profile is smoothed to obtain an angle of attack curve that meets the control quantity constraints; the angle of attack parameters are optimized and designed, and the trajectory planning problem is converted into a time parameter planning problem. The multi-constraint flight trajectory is obtained by online planning of the time parameters. Summary of the Invention

[0005] The present invention provides an aircraft trajectory planning method and related products taking into account terminal time and track deviation angle constraints.

[0006] The technical solution of the present invention is as follows: A method for aircraft trajectory planning considering terminal time and track angle constraints, comprising:

[0007] Step 101: Generate a flight state time series and a roll angle instruction time series according to a desired initial state and a desired terminal state;

[0008] Step 102: Iteratively update the flight status time series and the control input time series based on the current flight status time series, the current bank angle command time series, the terminal time constraint, and the terminal track angle constraint. If the proximity between two adjacent flight status time series meets the set requirements, the iteration is terminated and the latest flight status time series and the latest control input time series are output. Otherwise, the next round of update operation is performed.

[0009] The iterative operation is to calculate the following optimization problem:

[0010] ;

[0011] ;

[0012] in, is the state variable, is the distance from the center of the Earth, and The geocentric longitude and latitude are respectively, is the speed of the aircraft, is the aircraft track inclination angle, is the aircraft track deflection angle, is the roll angle of the aircraft, For time, is the objective function, is the reference state, is the terminal loss, For terminal time The reference state, For the initial moment The state variables, For the terminal moment The state variables, is the process loss function, the independent variable , , is the initial time;

[0013] in, , Is the function in reference state The value of and are the lift and drag forces on the aircraft, , , That is, the time derivative of the roll angle command, which is used as the control variable. , is the value of the function in the reference state, is the Earth's rotation angular velocity,

[0014] in, is the desired initial state, is the desired terminal state, Indicates the value range constraint of the state variable, is the upper limit of the amplitude of the roll angle change rate, In order to make the iterative process satisfy the small perturbation linearization principle;

[0015] Among them, n takes the values ​​of 1, 2, and 3, which respectively represent are heat flux, dynamic pressure and overload, is the upper limit of the corresponding quantity, and They are the distance from the center of the Earth and the velocity in the reference state, respectively.

[0016] Optionally, the heat flux , is the heat transfer coefficient of the aircraft surface, is the atmospheric density.

[0017] Optionally, dynamic pressure , is the atmospheric density.

[0018] Optionally, overload , is the square of the mean lift force, is the square of the mean resistance, is the nominal acceleration due to gravity.

[0019] Optionally, ,in, For resistance About the distance from the center of the earth The partial derivative of For resistance About speed The partial derivative of Lift About the distance from the center of the earth The partial derivative of Lift About speed The partial derivative of .

[0020] Optionally, step 101 includes: starting from a desired initial state, continuing the roll angle direction of the previous guidance cycle in each guidance cycle, executing a longitudinal guidance law to search for a roll angle magnitude, executing a lateral guidance law to determine a sign of the roll angle, generating a roll angle command based on the roll angle magnitude determined by the longitudinal guidance law and the sign of the roll angle determined by the lateral guidance law, and numerically integrating the roll angle command and a state of the aircraft at the end of the previous guidance cycle to obtain a state of the aircraft at the end of the current guidance cycle;

[0021] Determine whether the degree of proximity between the aircraft state and the desired terminal state at the end of the current guidance cycle meets the set requirements. If so, output the flight state time series and the bank angle command time series and end step 101. Otherwise, continue to the next guidance cycle.

[0022] Among them, the state variable in step 101 .

[0023] The technical solution of the present invention is as follows: an electronic device includes a memory and a processor, the memory stores a program, and the processor runs the program to execute the above-mentioned aircraft trajectory planning method considering terminal time and track deviation angle constraints.

[0024] The technical solution of the present invention is as follows: an aircraft, comprising a memory and a processor, wherein the memory stores a program, and the processor runs the program to execute the above-mentioned aircraft trajectory planning method considering terminal time and track deviation angle constraints.

[0025] The technical solution of the present invention is as follows: a program product, which executes the above-mentioned aircraft trajectory planning method considering terminal time and track deviation angle constraints when running.

[0026] By reconstructing state variables and convexifying the nonlinear trajectory planning problem (including convexifying the objective function, the dynamic equations, and the process constraints), the trajectory planning process is stabilized and the success rate of the solution is improved. Furthermore, the method of the present invention can simultaneously satisfy both terminal flight time constraints and terminal track deviation angle constraints. The method of the present invention can be used for trajectory planning for both independent aircraft and multi-aircraft systems. Furthermore, some embodiments can provide more reasonable initial trajectory guesses, further reducing the computational complexity of trajectory planning and improving the reliability of the results. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is an information flow diagram of the aircraft trajectory planning method considering terminal time and track deviation angle constraints of the present invention.

[0028] Figure 2It is a trajectory diagram of the aircraft trajectory planning method considering the terminal time and track deviation angle constraints of the present invention.

[0029] Figure 3 It is the detailed generation process of the initial trajectory guess. DETAILED DESCRIPTION

[0030] The present invention will be further described below with reference to specific embodiments, but the protection scope of the present invention is not limited thereto.

[0031] refer to Figure 1 The present invention's aircraft trajectory planning method, which considers terminal time and track deviation angle constraints, can be used for trajectory planning in a multi-aircraft system. The trajectory planning process for each aircraft is performed independently. Therefore, the present invention's method is also applicable to trajectory planning for a single aircraft.

[0032] From a software perspective, the execution subject of the method is a program. From a hardware perspective, the execution subject of the method is an electronic device or aircraft, specifically a processor therein.

[0033] Step 101: Generate a flight state time series and a roll angle instruction time series according to a desired initial state and a desired terminal state.

[0034] The flight status time series and the bank angle command time series constitute the initial trajectory guess.

[0035] The expected initial state is recorded as , the expected terminal state is recorded as The flight status time series obtained in this step is recorded as And the control input time series is recorded as , the subscripts of the two Indicates the The subscript 0 of the two indicates that they are the results of the 0th iteration of step 102 (i.e., the initial solution). i As the aircraft number.

[0036] In step 101, the motion of the aircraft from the desired initial state to the desired terminal state is divided into a plurality of consecutive guidance cycles. The magnitude and sign of the roll angle are considered constant during each guidance cycle. During each guidance cycle, the longitudinal guidance law is executed to search for the roll angle magnitude, and the lateral guidance law is executed to determine the roll angle sign. The roll angle magnitude and sign constitute the roll angle command. Subsequently, the aircraft's kinematic equations are numerically integrated based on the aircraft's state at the end of the previous guidance cycle and the roll angle command of the current guidance cycle to obtain the aircraft's state at the end of the current guidance cycle (which is also the aircraft's state at the beginning of the next guidance cycle). The calculations cease if the aircraft's state at the end of the current guidance cycle is sufficiently close to the desired terminal state (i.e., meets the terminal energy requirement).

[0037] Figure 3 The operation flow of the method of step 101 is shown. Figure 3 Make an introduction.

[0038] The longitudinal guidance law operates as follows.

[0039] Step 1011: Initialize the roll angle amplitude to , subscript Represents the longitudinal guidance law The result of the iteration.

[0040] Step 1012: Execute the longitudinal guidance law to determine the roll angle amplitude. In this step, the sign of the roll angle continues to use the sign of the roll angle at the end of the previous iteration cycle.

[0041] According to the current constant roll angle amplitude The aircraft dynamics equations such as formula (1) and (2) are numerically integrated with the sign of the roll angle determined at the end of the previous iteration cycle to predict the state of the aircraft when the integration termination condition is met, and the terminal state prediction value is obtained. , compare the terminal state prediction value and the desired terminal state , according to formula (3) we can get the range error .

[0042] Numerical integration can be performed using the classical Runge-Kutta integration method. Note: The black dot above the symbol indicates the time derivative.

[0043] (1)

[0044] (2)

[0045] Where, As the state variable of the differential equation, is the distance from the center of the Earth, and are the geocentric longitude and latitude, is the speed (rate) of the aircraft. is the aircraft track inclination angle, with reference to the local horizontal plane, with upward being positive; The control amount is the aircraft's roll angle. .

[0046] other, is the mass of the aircraft, is the acceleration due to gravity, is the angular velocity of the Earth's rotation. and are the lift and drag on the aircraft, which are calculated as follows:

[0047] ;

[0048] Where: is the atmospheric density, using the exponential atmospheric model Perform calculations, is the surface atmospheric density, is the height of the aircraft from the ground, , is the radius of the Earth, , in meters, is the characteristic area of ​​the aircraft, and They correspond to the lift coefficient and drag coefficient of the aircraft respectively.

[0049] (3)

[0050] Where, and Both indicate the range to be flown, the range to be flown The calculation adopts a three-dimensional calculation formula that takes into account both the arc length and height error of the sub-satellite point:

[0051]

[0052] Where: For the current state of the geocentric distance (the first item) and the geocentric latitude (the second item), calculate The terminal state will be predicted when Substitute the geocentric distance and geocentric latitude in ,calculate The terminal state is expected when Substitute the geocentric distance and geocentric latitude in .

[0053] Determine whether the range error is less than the set threshold, if so, output the current roll angle amplitude as the current Guidance cycle instructions Otherwise, Newton iteration method is used according to the current range error and the current roll angle amplitude Get the updated roll angle amplitude And return to step 1012.

[0054] The formula of Newton's iteration method is as follows:

[0055] ; is the tilt angle, g is the range error, and the subscripts of j The number representing the Newton iteration number in the current guidance cycle.

[0056] Step 1013: Execute the lateral guidance law to determine the sign of the roll angle in the current guidance cycle.

[0057] The lateral guidance law operates as follows.

[0058] , sgn(*) is the sign function, For the The sign of the bank angle within a guidance cycle, For the The heading angle error during a guidance cycle is, is the upper boundary threshold of the safety corridor, is the lower boundary threshold of the safety corridor, .

[0059] The principle of the lateral guidance law is that once the heading angle error formed by the aircraft velocity direction (heading angle) and the target position line of sight angle exceeds the safety corridor boundary, the sign of the bank angle needs to be reversed.

[0060] Step 1014: Numerically integrate the kinematic equations according to the roll angle amplitude determined in step 1012 and the roll angle sign determined in step 1013 to obtain the state at the end of the current guidance cycle.

[0061] Step 1015: Determine whether the state at the end of the current guidance cycle determined in step 1014 meets the terminal energy requirement. If so, step 101 ends; otherwise, update the state at the initial moment of the next guidance cycle and return to step 1012.

[0062] It should be noted that the initial trajectory guess can also be obtained using other existing techniques, such as interpolation of the desired initial state and the desired terminal state. The initial trajectory guess obtained by the method provided in this embodiment of the present invention better conforms to the dynamic and process constraints and is closer to the optimal solution, thereby reducing the computational complexity of subsequent step 102 and achieving a better result.

[0063] Step 102: Iteratively update the flight status time series and the control input time series based on the current flight status time series, the current bank angle command time series, the terminal time constraint, and the terminal track angle constraint. If the proximity between two adjacent flight status time series meets the set requirements, the iteration is terminated and the latest flight status time series and the latest control input time series are output. Otherwise, the next round of update operation is performed.

[0064] The iterative update adopts the sequential convex optimization method. The following shows the derivation process of this convex optimization problem.

[0065] (1) State variable reconstruction

[0066] In order to achieve the goal of decoupling the control quantity and the state quantity and specifying the terminal time and terminal track angle of the aircraft, the present invention introduces the roll angle and time As state variables, the state equation is formed:

[0067] .

[0068] The state variables of the new state equation are given by Updated to ,time As a state variable, the method is to define a new independent variable , , is the initial time, take =0, is the terminal time, and the control variable is given by Updated to , recorded as The new state equation is simplified into the following form, and it can be found that the decoupling of state quantity and control quantity is achieved, and the flight time The total flight time can be treated as a terminal constraint as a state variable:

[0069]

[0070]

[0071]

[0072] .

[0073] (2) Convex treatment of nonlinear trajectory planning problems

[0074] According to the state variables selected in step (1), the present invention forms a nonlinear trajectory planning problem in the form of , and the convexification of the problem will be realized next.

[0075]

[0076] is the terminal loss (Mayer term), is the process loss (Lagrange term). The endpoint constraints include the initial state constraints and terminal state constraints Path constraints include state boundary constraints , and It is a schematic symbolic representation of the lower and upper bounds of the state variable. The actual bound is the bound of a certain region of the vector space. . Process constraints include heat flux constraints , dynamic pressure constraint , overload constraint .

[0077] is a function representing the process loss, is the heat flux density, is the heat transfer coefficient of the aircraft surface, is the atmospheric density, is the maximum heat flux limit, It is dynamic pressure, is the maximum dynamic pressure that the structure can withstand, is the total overload, is the square of the mean lift force, is the square of the mean resistance, is the nominal acceleration due to gravity, It is the maximum overload that the aircraft can withstand.

[0078] 1. Convexification of the objective function

[0079] Mayer term Can be found at the reference terminal status point Linear approximation is performed at the Lagrange term in In the reference state The first-order Taylor expansion is performed at . The reference state when the convexification is first performed is The flight state time series in the initial trajectory guess generated in step 101 is used , No. The convexification of the second problem is to use the A convex optimization problem generates a time series of flight states As a reference state.

[0080] ;

[0081] ;

[0082] These two formulas are based on the convexification of the objective function by Taylor expansion. refers to the reference state selected during the sequential convex optimization process.

[0083] 2. Convexification of the dynamic equations

[0084] The dynamic equation after state variable reconstruction realizes the separation of control quantity and state quantity, so the highly nonlinear Can be in reference state Perform a first-order Taylor approximation, the specific form is:

[0085]

[0086]

[0087] .

[0088] in, For resistance About the distance from the center of the earth The partial derivative of For resistance About speed The partial derivative of Lift About the distance from the center of the earth The partial derivative of Lift About speed The partial derivative of .

[0089] 3. Convexification of process constraints

[0090] Three process constraints in the optimization problem , dynamic pressure , overload Can be expressed as state quantity Function, remember , so it is convexed in a similar way:

[0091]

[0092] ;

[0093] is the distance from the center of the Earth in the reference state, is the reference state rate, is the radius of the Earth, , unit is meter.

[0094] Sequential Convex Optimization Algorithm The iterative process is converted to:

[0095]

[0096]

[0097] is the heat flux constraint , dynamic pressure constraint , overload constraint The result of the three convexification processes. Endpoint constraints include initial state constraints and terminal state constraints Path constraints include state boundary constraints , control quantity boundary constraint , To make the iterative process satisfy the small perturbation linearization principle.

[0098] The convexification of the objective function, dynamic equations and process constraints is based on the first-order Taylor approximation, which requires the introduction of the form The inequality constraints of the optimization process are used to ensure the approximation accuracy, so that the optimization process satisfies the small perturbation linearization principle, thereby ensuring that the solution of the successive convex optimization problem can closely approximate the solution of the original nonlinear optimization problem. The method proposed in this paper transforms the non-convex problem into a convex optimization problem, greatly reducing the computational difficulty.

[0099] Step 103: Evaluate the degree of closeness between the current flight status time series and the flight status time series of the previous round. If the closeness between the two meets the set standard, output the current flight status time series and the current control input time series; otherwise, go to step 102.

[0100] Specifically, if the following formula is satisfied, it indicates that the closeness meets the set standard. , is the allowable error for algorithm convergence, and is the flight status time series, its superscript is the number of iterations, and sup is the supremum symbol.

[0101] By reconstructing state variables and convexifying the nonlinear trajectory planning problem (including convexifying the objective function, the dynamic equations, and the process constraints), the trajectory planning process is stabilized and the success rate of the solution is improved. Furthermore, the method of the present invention simultaneously satisfies both terminal flight time constraints and terminal track deviation angle constraints. The method of the present invention can be used for trajectory planning for both independent aircraft and multi-aircraft systems. Furthermore, some embodiments can provide more reasonable initial trajectory guesses, further reducing the computational complexity of trajectory planning and improving the reliability of the results.

[0102] refer to Figure 2 The method of the present invention can be applied to trajectory planning of multi-aircraft collaborative missions. Aircraft 1 to Aircraft n The trajectory planning of each aircraft is calculated independently. i The terminal time of each aircraft Expected end time , terminal track deviation angle is the expected terminal track deviation angle This method can be used to achieve terminal flight coordination and terminal angle coordination (i.e., terminal track deviation coordination) of multiple aircraft. Each aircraft can ultimately plan a trajectory that satisfies its own terminal flight time and terminal track deviation.

[0103] Based on the same inventive concept, the present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a program, and the processor runs the program to execute the above-mentioned aircraft trajectory planning method considering terminal time and track deviation angle constraints.

[0104] Based on the same inventive concept, the present invention also provides an aircraft, including a memory and a processor, wherein the memory stores a program, and the processor runs the program to execute the above-mentioned aircraft trajectory planning method considering terminal time and track deviation angle constraints.

[0105] Based on the same inventive concept, the present invention also provides a program product, which executes the above-mentioned aircraft trajectory planning method considering the terminal time and track deviation angle constraints when running.

[0106] The above memory is, for example, a USB flash drive, a hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc., which can store program codes.

[0107] The above processors are, for example, a central processing unit (CPU), a graphics processing unit (GPU), etc. The number of processors can be one or more, and they can be deployed on the same computing device or on different computing devices.

[0108] The various embodiments of the present invention are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments.

[0109] The scope of protection of the present invention is not limited to the above-described embodiments. Obviously, those skilled in the art may make various modifications and variations to the present invention without departing from the scope and spirit of the present invention. If such modifications and variations fall within the scope of the claims of the present invention and their equivalents, the present invention is intended to include such modifications and variations.

Claims

1. A method for aircraft trajectory planning considering terminal time and track angle constraints, characterized in that: include: Step 101: Generate a flight state time series and a roll angle instruction time series according to a desired initial state and a desired terminal state; Step 102: Iteratively update the flight status time series and the control input time series based on the current flight status time series, the current bank angle command time series, the terminal time constraint, and the terminal track angle constraint. If the proximity between two adjacent flight status time series meets the set requirements, the iteration is terminated and the latest flight status time series and the latest control input time series are output. Otherwise, the next round of update operation is performed. The iterative operation is to calculate the following optimization problem: ； ； in, is the state variable, is the distance from the center of the Earth, and The geocentric longitude and latitude are respectively, is the speed of the aircraft, is the aircraft track inclination angle, is the aircraft track deflection angle, is the roll angle of the aircraft, For time, is the objective function, is the reference state, is the terminal loss, For terminal time The reference state, For the initial moment The state variables, For the terminal moment The state variables, is the process loss function, the independent variable , ; in, , Is the function in reference state The value of and are the lift and drag forces on the aircraft, , , That is, the time derivative of the roll angle command, which is used as the control variable. , is the value of the function in the reference state, is the Earth's rotation angular velocity, in, is the desired initial state, is the desired terminal state, Indicates the value range constraint of the state variable, is the upper limit of the amplitude of the roll angle change rate, In order to make the iterative process satisfy the small perturbation linearization principle; Among them, n takes the values ​​of 1, 2 and 3 to represent are heat flux, dynamic pressure and overload, is the upper limit of the corresponding quantity, and They are the distance from the center of the Earth and the velocity in the reference state, respectively.

2. The method according to claim 1, characterized in that Heat flux , is the heat transfer coefficient of the aircraft surface, is the atmospheric density.

3. The method according to claim 1, characterized in that dynamic pressure , is the atmospheric density.

4. The method according to claim 1, wherein Overload , is the square of the mean lift force, is the square of the mean resistance, is the nominal acceleration due to gravity.

5. The method according to claim 1, wherein ； in, For resistance About the distance from the center of the earth The partial derivative of For resistance About speed The partial derivative of Lift About the distance from the center of the earth The partial derivative of Lift About speed The partial derivative of .

6. The method according to claim 1, characterized in that Step 101 includes: Starting from a desired initial state, in each guidance cycle, continuing the roll angle direction of the previous guidance cycle, executing the longitudinal guidance law to search for a roll angle magnitude, executing the lateral guidance law to determine a roll angle sign, generating a roll angle command based on the roll angle magnitude determined by the longitudinal guidance law and the roll angle sign determined by the lateral guidance law, and numerically integrating the roll angle command and the vehicle state at the end of the previous guidance cycle to obtain a vehicle state at the end of the current guidance cycle; Determine whether the degree of proximity between the aircraft state and the desired terminal state at the end of the current guidance cycle meets the set requirements. If so, output the flight state time series and the bank angle command time series and end step 101. Otherwise, continue to the next guidance cycle. Among them, the state variable in step 101 .

7. An electronic device, characterized in that: The invention comprises a memory and a processor, wherein the memory stores a program, and the processor runs the program to execute the aircraft trajectory planning method considering the terminal time and track deviation angle constraints according to any one of claims 1 to 6.

8. An aircraft, characterized in that: The invention comprises a memory and a processor, wherein the memory stores a program, and the processor runs the program to execute the aircraft trajectory planning method considering the terminal time and track deviation angle constraints according to any one of claims 1 to 6.

9. A program product, characterized in that When running, the program product executes the aircraft trajectory planning method considering terminal time and track deviation angle constraints according to any one of claims 1 to 6.

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