Multi-aircraft collaborative reentry trajectory planning method, system, electronic equipment and medium

Abstract

The present invention relates to a method, system, electronic device and medium for collaborative reentry trajectory planning of multiple aircraft, and belongs to the field of aircraft trajectory planning. The method first establishes a dynamic model of the aircraft, and improves the dynamic model by redefining independent variables; establishes a terminal time constraint according to the improved aircraft dynamic model, and determines and processes the trajectory planning problem model by adding other constraints of the aircraft to obtain the processed trajectory planning problem model; generates an available initial reference trajectory according to the desired initial and terminal conditions, and combines the processed trajectory planning problem model to determine the collaborative reentry trajectory of multiple aircraft using a sequential convex optimization method. The method of the present invention can solve the collaborative reentry trajectory planning problem of multiple hypersonic gliding vehicles, and improve the efficiency and accuracy of collaborative reentry trajectory planning of multiple aircraft.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft trajectory planning, and in particular to a method, system, electronic equipment and medium for collaborative re-entry trajectory planning of multiple aircraft. Background Art

[0002] Hypersonic Gliding Vehicle (HGV) is a near-space aircraft with high speed, large-scale maneuvering and long-range gliding capabilities, wide combat range, strong penetration capability, etc., and has broad application prospects. In order to counter missile defense systems, it is necessary to improve the penetration capability of HGV. However, with the development of air defense weapon systems, the defense and interception capabilities of a single hypersonic aircraft are becoming increasingly stronger, which has greatly limited its strike effect. In this context, it is more necessary to develop collaborative combat technology for multiple hypersonic aircraft. Multi-aircraft collaborative combat strikes can greatly increase the interception difficulty of the defense system and achieve saturation attacks on the target. For hypersonic gliding vehicles, which have large uncertainty in the flight environment, drastic time-varying parameters, and severe coupling, trajectory planning and tracking control under multi-constraint collaborative strikes are more challenging.

[0003] The study of trajectory planning for the reentry phase of a hypersonic vehicle is a nonlinear programming problem with complex multi-constraints. In early studies, the state profile of the planned trajectory was a common method, and many results have been achieved in continuous improvement. It is worth noting that real-time performance is crucial in HGV collaborative trajectory optimization. Convex optimization methods have been widely used in the field of trajectory optimization due to their good convergence performance and wide applicability. Trajectory optimization problems with complex constraints and nonlinear dynamics can be transformed into a series of convex optimization problems through convexification techniques.

[0004] Most of the research on the coordinated reentry guidance problem of multiple hypersonic vehicles focuses on achieving time coordination in the reentry phase. The current main method is to analyze and design the corresponding relationship between the reentry flight time and each state quantity, and correct the flight trajectory to achieve the desired time coordination. However, it cannot directly control the terminal time, which wastes the number of solutions. Moreover, its objective function is committed to ensuring the terminal constraints and cannot meet better performance indicators such as minimum thermal flux overload. Therefore, the problem of coordinated reentry trajectory optimization for multiple vehicles needs further attention and research. Summary of the invention

[0005] In order to solve or at least alleviate the above problems, the present invention proposes a multi-aircraft collaborative re-entry trajectory planning method, system, electronic equipment and medium to improve the efficiency and accuracy of multi-aircraft collaborative re-entry trajectory planning.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] In one aspect, the present invention provides a multi-aircraft collaborative reentry trajectory planning method, comprising:

[0008] Establishing a dynamic model of the aircraft, and improving the dynamic model by redefining independent variables to generate an improved dynamic model of the aircraft;

[0009] Establishing terminal time constraints according to the improved aircraft dynamics model, and adding other constraints of the aircraft to determine the trajectory planning problem model;

[0010] Processing the trajectory planning problem model to obtain a processed trajectory planning problem model;

[0011] Generate a usable initial reference trajectory based on desired initial and terminal conditions;

[0012] According to the processed trajectory planning problem model and the initial reference trajectory, a sequential convex optimization method is used to determine the multi-aircraft cooperative reentry trajectory.

[0013] Optionally, the establishing of a dynamic model of a hypersonic glide vehicle and improving the dynamic model by redefining independent variables to generate an improved dynamic model of the vehicle specifically includes:

[0014] A dynamic model of a hypersonic glide vehicle is established; the dynamic model uses a kinematic equation with time t as an independent variable to describe the unpowered glide process of the vehicle during reentry;

[0015] By redefining the normalized time τ∈[0,1] as an independent variable, the dynamic model is improved to generate an improved aircraft dynamic model where x=[r,θ,φ,v,γ,ψ,σ,t] T is the flight state vector; r is the distance from the center of the earth to the aircraft, θ and φ represent longitude and latitude respectively, v is the flight speed of the aircraft relative to the earth, γ and ψ are the ballistic inclination angle and velocity heading angle respectively, and σ is the roll angle; u σ is the rate of change of the roll angle; time control quantity f(x,u σ ) and f Ω (x,u σ ) respectively represent the terms without and with the earth's rotation angular velocity in the improved aircraft dynamics model.

[0016] Optionally, establishing the terminal time constraint according to the improved aircraft dynamics model and adding other constraints of the aircraft to determine the trajectory planning problem model specifically includes:

[0017] The terminal time constraint is established according to the improved aircraft dynamics model, and the trajectory planning problem model P0 is determined by adding other constraints of the aircraft. Where J represents the optimization function, represents the heat flux density; They are the heat flux densities that the aircraft can withstand. The dimensionless maximum values ​​of overload n and dynamic pressure q; g1-g3 represent the functional expressions of the constraints, K Q is the heat flux density constant, ρ is the atmospheric density, L and D are the lift and drag accelerations respectively; σ max is the limit value of the roll angle; u σmax is the limit value of the rate of change of the roll angle; is the expected total flight time; r0,θ0,φ0,v0,γ0,ψ0 represent the initial state quantities respectively; r f ,θ f ,φ f ,v f ,γ f ,ψ f They represent the terminal state quantities respectively; v fmin , v fmax represent the minimum and maximum expected terminal velocities, respectively.

[0018] Optionally, the processing the trajectory planning problem model to obtain a processed trajectory planning problem model specifically includes:

[0019] Based on the small perturbation linearization method, the trajectory planning problem model is linearized and convexified, and the trajectory planning problem model P0 is converted into a continuous convex optimization problem model P1;

[0020] The continuous convex optimization problem model P1 is discretized to obtain a processed trajectory planning problem model P2.

[0021] Optionally, generating an available initial reference trajectory according to desired initial and terminal conditions specifically includes:

[0022] Determine the initial sequence of control variables based on the desired initial and terminal conditions in and They represent the roll angle change rate control amount and time control amount of discrete point i respectively;

[0023] The initial sequence of control variables is substituted into the trajectory planning problem model P0, and a usable initial reference trajectory is generated through fourth-order Runge-Kutta numerical integration.

[0024] On the other hand, the present invention also provides a multi-aircraft collaborative reentry trajectory planning system, comprising:

[0025] The aircraft modeling and model improvement module is used to establish a dynamic model of the aircraft and improve the dynamic model by redefining independent variables to generate an improved aircraft dynamic model;

[0026] A trajectory planning problem model building module is used to establish a terminal time constraint according to the improved aircraft dynamics model, and to add other constraints of the aircraft to determine the trajectory planning problem model;

[0027] A trajectory planning problem model processing module, used to process the trajectory planning problem model to obtain a processed trajectory planning problem model;

[0028] An initial reference trajectory generation module, used to generate a usable initial reference trajectory according to desired initial and terminal conditions;

[0029] The collaborative reentry trajectory solving module is used to determine the collaborative reentry trajectory of multiple aircraft using a sequential convex optimization method based on the processed trajectory planning problem model and the initial reference trajectory.

[0030] On the other hand, the present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the multi-aircraft collaborative re-entry trajectory planning method when executing the computer program.

[0031] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, and when the computer program is executed, the multi-aircraft collaborative re-entry trajectory planning method is implemented.

[0032] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0033] The present invention provides a method, system, electronic device and medium for collaborative reentry trajectory planning of multiple aircraft. The method comprises: establishing a dynamic model of an aircraft, and improving the dynamic model by redefining independent variables to generate an improved aircraft dynamic model; establishing a terminal time constraint according to the improved aircraft dynamic model, and determining a trajectory planning problem model by attaching other constraints of the aircraft; processing the trajectory planning problem model to obtain a processed trajectory planning problem model; generating an available initial reference trajectory according to the desired initial and terminal conditions; and determining the collaborative reentry trajectory of multiple aircraft using a sequential convex optimization method according to the processed trajectory planning problem model and the initial reference trajectory. The method of the present invention improves the dynamic model by redefining independent variables, and the improved aircraft dynamic model can directly control the terminal time, thereby improving the efficiency of collaborative reentry trajectory planning of multiple aircraft; and the trajectory planning problem model determined by the method of the present invention selects the minimum heat flux overload as the optimization objective function, which can meet better performance indicators such as the minimum heat flux overload, thereby improving the accuracy of collaborative reentry trajectory planning of multiple aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0035] Figure 1 A flowchart of a multi-aircraft collaborative reentry trajectory planning method provided by an embodiment of the present invention;

[0036] Figure 2 A schematic diagram of a curve showing changes in altitude, speed, trajectory inclination and heading angle over time at three given terminal times provided in an embodiment of the present invention;

[0037] Figure 3 A schematic diagram of a roll angle command curve under three given terminal times provided in an embodiment of the present invention;

[0038] Figure 4 A schematic diagram of ground projection of flight trajectories at three given terminal times provided by an embodiment of the present invention;

[0039] Figure 5 A schematic diagram of a curve showing changes in altitude, speed, trajectory inclination and heading angle of two aircraft over time provided by an embodiment of the present invention;

[0040] Figure 6 A schematic diagram of ground projection of the flight trajectories of two aircraft provided in an embodiment of the present invention;

[0041] Figure 7 A schematic diagram of an optimization process curve of the objective function of two aircrafts provided in an embodiment of the present invention;

[0042] Figure 8 A schematic diagram of the simulation results of the flight trajectories of two aircrafts provided in an embodiment of the present invention;

[0043] Fig. 9 A schematic diagram of the structure of a multi-aircraft collaborative re-entry trajectory planning system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0045] The purpose of the present invention is to provide a method, system, electronic equipment and medium for collaborative re-entry trajectory planning of multiple aircraft, which can solve the problem of collaborative re-entry trajectory planning of multiple hypersonic gliding vehicles and improve the efficiency and accuracy of collaborative re-entry trajectory planning of multiple aircraft.

[0046] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] Figure 1 Flow chart of the multi-aircraft cooperative reentry trajectory planning method provided by an embodiment of the present invention. Figure 1 The present invention provides a multi-aircraft collaborative reentry trajectory planning method comprising:

[0048] Step 101: Establish a dynamic model of an aircraft, and improve the dynamic model by redefining independent variables to generate an improved dynamic model of the aircraft.

[0049] In step 101, the classic hypersonic glide vehicle (referred to as the vehicle) reentry dynamics equation is first established as the dynamics model of the vehicle, and then the original equation is improved to achieve terminal time freedom and controllability, thereby generating an improved vehicle dynamics model.

[0050] The step 101 establishes a dynamic model of a hypersonic glide vehicle, and improves the dynamic model by redefining independent variables to generate an improved dynamic model of the vehicle, specifically including:

[0051] Step 1.1: Establish a dynamic model of a hypersonic glide vehicle. The dynamic model uses a kinematic equation with time t as the independent variable to describe the unpowered glide process of the vehicle during reentry. Assuming that the earth is a sphere and considering its rotation, the dimensionless equation of the dynamic model is as follows:

[0052] dr / dt=vsinγ

[0053] dθ / dt=vcosγsinψ / (rcosφ)

[0054] dφ / dt=vcosγcosψ / r

[0055] dv / dt=-D-sinγ / r 2 +Ω 2 rcosφ(sinγcosφ-cosγsinφcosψ)

[0056] dγ / dt=[Lcosσ-cosγ / r 2 +v 2 cosγ / r+2Ωvcosφsinψ+Ω 2 rcosφ(cosγcosφ+sinγsinφcosψ)] / v

[0057] dψ / dt=[Lsinσ / cosγ+v 2 cosγsinψtanφ / r-2Ωv(tanγcosφcosψ-sinφ)+Ω 2 rsinφcosφsinψ / cosγ] / v

[0058] dσ / dt=u σ

[0059] The distance r from the center of the earth to the aircraft in the equation is dimensionless by the average radius of the earth R0 = 6378140m. The state quantities θ and φ are longitude and latitude respectively. v is the flight speed relative to the earth, which is Dimensionless, g0 = 9.807 m / s 2 is the gravitational acceleration on the earth’s surface. γ and ψ are the ballistic inclination angle and velocity heading angle, respectively. The constant Ω is the earth’s rotational angular velocity, which is The independent variable time t is non-dimensionalized. Dimensionless. σ is the roll angle. In order to ensure flight stability, the change rate of the roll angle u is selected σ As a control quantity, it is Dimensionless. L and D are the lift and drag accelerations dimensionless by g0, respectively. They are specifically expressed as:

[0060]

[0061] Where m is the dimensionless mass of the aircraft, and the atmospheric density ρ = ρ0exp(-h / h s ) is a function of the flight altitude, where h s =7200m, S A is the aircraft reference area, C L , C D They are respectively the lift coefficient and the drag coefficient of the aircraft, which are related to the angle of attack and the Mach number of the aircraft. The present invention designs the angle of attack-velocity profile as a commonly used piecewise function.

[0062] Step 1.2: By redefining the normalized time τ∈[0,1] as an independent variable, the dynamic model is improved to generate an improved aircraft dynamic model where x=[r,θ,φ,v,γ,ψ,σ,t] T is the flight state vector; r is the distance from the center of the earth to the aircraft, θ and φ represent longitude and latitude respectively, v is the flight speed of the aircraft relative to the earth, γ and ψ are the ballistic inclination angle and velocity heading angle respectively, and σ is the roll angle; u σ is the rate of change of the roll angle; time control quantity f(x,u σ ) and f Ω (x,u σ ) respectively represent the terms without and with the earth's rotation angular velocity in the improved aircraft dynamics model.

[0063] The present invention improves the dynamic model of the aircraft by redefining the independent variables. Assuming that the initial and final times of the flight are t0 and t f , redefine the normalized time τ∈[0,1] as the independent variable, map the time interval of the original equation to [0,1], and introduce the time control variable u t =t f -t0, so the actual dimensionless time t can be expressed as:

[0064] t=t0+(t f -t0)τ,τ∈[0,1]

[0065] Then, the dimensionless time t of the original independent variable is taken as the new state quantity, and its differential equation relative to the normalized time τ is obtained as follows:

[0066]

[0067] Now let the flight state vector be x = [r,θ,φ,v,γ,ψ,σ,t] T , separating the terms with the angular velocity of the earth's rotation, the system of dynamic differential equations can be written as follows:

[0068]

[0069] Among them, f(x,u σ ) represents the part without the angular velocity of the earth's rotation, f Ω (x,u σ ) represents the part with the angular velocity of the earth's rotation, and is composed of f1-f6 and f Ω4 -f Ω6 Represents the terms in each equation. The above equations give the motion equation with τ as the independent variable as the improved aircraft dynamics model, which can be expressed as:

[0070]

[0071] where u t This is the newly added time control amount.

[0072] Step 102: Establish terminal time constraints based on the improved aircraft dynamics model, and add other constraints of the aircraft to determine the trajectory planning problem model.

[0073] The classic reentry path constraint of a spacecraft can be expressed as:

[0074]

[0075] in They are the heat flux densities that the aircraft can withstand. The dimensionless maximum values ​​of overload n and dynamic pressure q. g1-g3 represent the functional expressions of the constraints, K Q is the heat flux density constant, ρ is the atmospheric density, and L and D are the lift and drag accelerations, respectively.

[0076] In order to accurately meet the coordination constraint of the total reentry flight time, the control quantity u t It needs to be set to the desired flight time and maintained throughout the entire process. At the same time, the aircraft's roll angle and its rate of change should be limited to a certain range to ensure the stability of the aircraft's attitude.

[0077]

[0078] Where σ is the roll angle, σ max is the limit value of the roll angle; select the rate of change of the roll angle u σ As the control quantity, u σmax is the limit value of the rate of change of the roll angle; u t is the time control quantity, is the expected total flight time.

[0079] The optimization process restricts the initial and final states of the hypersonic glide vehicle during the re-entry phase, mainly targeting its altitude, longitude and latitude, speed, ballistic inclination and heading angle, in order to achieve multi-state collaborative planning.

[0080]

[0081] Among them, r0,θ0,φ0,v0,γ0,ψ0 represent the initial state quantities, r f ,θ f ,φ f ,v f ,γ f ,ψ f They represent the terminal state quantities respectively. fmin , v fmax represent the minimum and maximum expected terminal velocities, respectively.

[0082] The present invention selects the minimum thermal flux overload as the optimization objective function. Combining the above equations and inequality constraints, the collaborative reentry trajectory planning with flight time constraints can be described as the following non-convex optimal control problem:

[0083] P0

[0084]

[0085] subject to:

[0086] Where J represents the optimization function, represents the heat flux density. The state vector is x = [r,θ,φ,v,γ,ψ,σ,t] T , the control quantity is [u t ,u σ ] T , τ is the normalized time, f(x,u σ ) and f Ω (x,u σ ) is the dynamic equation of the system, They are the heat flux densities that the aircraft can withstand. The dimensionless maximum values ​​of overload n and dynamic pressure q. g1-g3 represent the functional expressions of the constraints, K Q is the heat flux constant, ρ is the atmospheric density, L and D are the lift and drag accelerations, respectively. R is the distance from the center of the earth to the aircraft, and the state quantities θ and φ are the longitude and latitude, respectively. v is the flight speed relative to the earth, γ and ψ are the ballistic inclination angle and velocity heading angle, respectively. The constant Ω is the angular velocity of the earth's rotation, σ is the roll angle, σ max is the limit value of the roll angle; the rate of change of the roll angle u σ As the control quantity, u σmax is the limit value of the rate of change of the roll angle; ut is the time control quantity, is the expected total flight time. r0,θ0,φ0,v0,γ0,ψ0 represent the initial state quantities, r f ,θ f ,φ f ,v f ,γ f ,ψ f They represent the terminal state quantities respectively. fmin , v fmax They represent the minimum and maximum values ​​of the expected terminal velocity respectively. P0 is the determined trajectory planning problem model.

[0087] Step 103: Process the trajectory planning problem model to obtain a processed trajectory planning problem model.

[0088] The trajectory planning problem model P0 determined in step 102 is a highly nonlinear optimal control problem. This step 103 approximates the non-convex expression based on the small perturbation linearization method; then discretizes it to convert it into a finite-dimensional second-order cone problem that can be solved by a sequential convex optimization method.

[0089] The step 103 processes the trajectory planning problem model to obtain a processed trajectory planning problem model, which specifically includes:

[0090] Step 3.1: Linearize and convexify the trajectory planning problem model based on the small perturbation linearization method, and convert the trajectory planning problem model P0 into a continuous convex optimization problem model P1;

[0091] The dynamic equations, process constraints and optimization objective functions are all non-convex. Given a fixed historical state They can be linearized by a first-order Taylor expansion at this point according to small perturbation linearization theory.

[0092] In the motion equation, the control quantity and the state quantity are coupled. Therefore, it is necessary to refer to the first-order Taylor expansion of multivariate functions for linearization. Ω (x,u) represent the terms without and with the angular velocity of the earth's rotation in the dynamic equations, respectively. Ω The value of the (x,u) part is relatively small and can be directly approximated by a fixed reference state: The linearization result of the dynamic equation is:

[0093]

[0094] in

[0095] Nonlinear path constraint gj (r, v) are functions related to the distance r from the center of the earth and the velocity v, which can be expressed by the following formula for a given state Linearization:

[0096]

[0097] in

[0098] In addition, in order to minimize the approximation error and ensure that the optimization variable takes values ​​near the given reference point, a trust region constraint is introduced, where δ is the size of the trust region:

[0099]

[0100] The integral objective function can also be linearized by referring to the above formula. After processing, the trajectory planning problem model P0 is converted into a continuous convex optimization problem model P1.

[0101] P1:

[0102] subject to:

[0103] Where J represents the optimization function, represents the heat flux density. The state vector is x = [r,θ,φ,v,γ,ψ,σ,t] T , the control quantity is u=[u t ,u σ ] T , τ is the normalized time, and F(x,u) and F Ω (x,u) represent the terms without and with the angular velocity of the earth's rotation in the dynamic equations, respectively. g1-g3 represent the function expressions of constraints, r is the distance from the center of the earth to the aircraft, the state quantities θ and φ are longitude and latitude respectively. v is the flight speed relative to the earth, γ and ψ are the ballistic inclination angle and velocity heading angle respectively. σ is the roll angle, σ max is the limit value of the roll angle; the rate of change of the roll angle u σ As the control quantity, u σmax is the limit value of the rate of change of the roll angle; u t is the time control quantity, is the expected total flight time. r0,θ0,φ0,v0,γ0,ψ0 represent the initial state quantities, r f ,θ f ,φ f ,v f ,γ f ,ψ fThey represent the terminal state quantities respectively. fmin , v fmax represent the minimum and maximum expected terminal velocities, respectively. represents the reference state of the state vector x, and δ is the size of the trust region.

[0104] Step 3.2: Discretize the continuous convex optimization problem model P1 to obtain a processed trajectory planning problem model P2.

[0105] In order to obtain the numerical solution of the continuous optimal control problem P1, it needs to be discretized. The present invention adopts the trapezoidal discretization method, firstly divides the normalized time domain into N equal intervals, generates N+1 independent variable nodes, and the step length of each segment is Δτ=1 / N. All discrete independent variable nodes are represented as {τ0,τ1,τ2,...,τ N}, where τ i =τ i-1 +Δτ,i=1,2,...,N. Then the state and control quantities corresponding to each node are discretized into a sequence {x0,x1,x2,...,x N} and {u0,u1,u2,...,u N Based on the above sequence, the kinetic equation can be numerically integrated as follows:

[0106]

[0107] Among them, k represents the number of iterations, and the result of the previous iteration is used as the reference state of this solution, which is Δτ is the discrete step length, and the state vector is x = [r,θ,φ,v,γ,ψ,σ,t] T , the control quantity is u=[u t ,u σ ] T , τ is the normalized time, and F(x,u) and F Ω (x,u) represent the terms without and with the angular velocity of the earth's rotation in the dynamic equations, respectively.

[0108] At the same time, other constraints are also discretized and can be expressed as:

[0109]

[0110]

[0111]

[0112] In the formula, the variables with the k-1 superscript all represent the values ​​in the last iteration and are used as reference values ​​here. g1-g3 represent the function expressions of the constraints, σ is the roll angle, σ max is the limit value of the roll angle; the rate of change of the roll angle u σ As the control quantity, u σmax is the limit value of the rate of change of the roll angle; u t is the time control quantity, is the expected total flight time. r is the distance from the center of the Earth to the vehicle, v is the flight speed relative to the Earth, represents the reference state of the state vector x, and δ is the size of the trust region.

[0113] The heat flux load Q accumulated over time during flight is also integrated using the trapezoidal method:

[0114]

[0115] Where Δτ is the discrete step length, Q i is the heat flux load of each discrete point, g1(r,v) represents the process constraint formula of heat flux density, r is the distance from the center of the earth to the aircraft, and v is the flight speed relative to the earth.

[0116] Then P1 is described as a discrete convex optimization subproblem, thus obtaining the processed trajectory planning problem model P2:

[0117] P2

[0118]

[0119] subject to:

[0120] In the formula, J represents the optimization function, Q N is the heat flow load of the Nth discrete point, i represents the sequence number of the discrete point, and the state vector is x = [r, θ, φ, v, γ, ψ, σ, t] T , the control quantity is u=[u t ,u σ ] T , Δτ is the discrete step length, τ is the normalized time, and F(x,u) and F Ω (x,u) represent the terms without and with the angular velocity of the earth's rotation in the dynamic equations, respectively. g1-g3 represent the function expressions of constraints, σ is the roll angle, σ max is the limit value of the roll angle; the rate of change of the roll angle u σAs the control quantity, u σmax is the limit value of the rate of change of the roll angle; u t is the time control quantity, is the expected total flight time. r is the distance from the center of the earth to the aircraft, v is the flight speed relative to the earth, the state quantities θ and φ are longitude and latitude respectively, and γ and ψ are the ballistic inclination angle and velocity heading angle respectively. r0, θ0, φ0, v0, γ0, ψ0 represent the initial state quantities, r f ,θ f ,φ f ,v f ,γ f ,ψ f They represent the terminal state quantities respectively. fmin , v fmax They represent the minimum and maximum expected terminal velocities, respectively. k-1 represents the reference state of the state vector x, and δ is the size of the trust region.

[0121] Step 104: Generate a usable initial reference trajectory based on the desired initial and terminal conditions.

[0122] The step 104 generates an available initial reference trajectory according to the desired initial and terminal conditions, specifically including:

[0123] Step 4.1: Determine the initial sequence of control variables based on the desired initial and terminal conditions in and They represent the roll angle change rate control amount and time control amount of discrete point i respectively.

[0124] The planning method of the initial trajectory uses energy as the independent variable, defines the concept of maneuver coefficient to describe the coupling relationship between the lateral and longitudinal trajectories, and then adjusts the directional angle deviation corridor in the lateral direction and controls the roll angle reversal to achieve the desired lateral maneuver. However, the state set at this time does not include the flight time, so according to the aircraft dynamics model, the time corresponding to each node in the trajectory is obtained according to the following formula. Note that this numerical integration trajectory includes M+1 corresponding energy nodes.

[0125]

[0126] Where i = 0, 1, ..., M represents the serial number of each discrete point, and the subscripts i and i + 1 represent the state quantity at that moment, {t0, t1, ..., t M} represents the time series, r is the distance from the center of the earth to the aircraft, v is the flight speed relative to the earth, and γ is the ballistic inclination angle.

[0127] Then the obtained time series {t0,t1,...,t M} and the corresponding roll angle sequence {σ0,σ1,...,σ M} Perform linear interpolation at equal time intervals. Then we can get the roll angle state sequence corresponding to the equal time interval arrangement

[0128] The flight terminal time of the initial trajectory is t M , and the expected terminal time t of the solution process f * Can be in t M , but it cannot be adjusted too much to avoid conflicts between the initial trajectory and other constraints, which will cause the iterative solution to fail. Note that due to the limitations of the initial trajectory generation method, its terminal state can have a certain difference from the expected terminal state, but it can be within the allowable range for the same reason as above. According to the terminal state constraints, the initial sequence of control variables can be determined Next, considering the limit constraint, the initial sequence of the roll angle change rate is obtained:

[0129]

[0130] in, is the roll angle state sequence element arranged at equal time intervals, u t,i is the time control quantity of discrete point i, represents the roll angle change rate control value of discrete point i and serves as the initial iterative trajectory. Δτ represents the discrete time step length.

[0131] Step 4.2: Substitute the initial sequence of control variables into the trajectory planning problem model P0, and generate a usable initial reference trajectory through fourth-order Runge-Kutta numerical integration.

[0132] The initial sequence of control quantities obtained in step 4.1 above Substituting into the dynamic equation, through the fourth-order Runge-Kutta numerical integration, the state sequence x corresponding to the equation of this paper is obtained again for the initial trajectory (0) As an available initial reference trajectory. Note that the above variables need to be dimensionless in advance.

[0133] Step 105: Determine the multi-aircraft cooperative reentry trajectory using a sequential convex optimization method based on the processed trajectory planning problem model and the initial reference trajectory.

[0134] Next, we introduce the solution process of sequential convex optimization.

[0135] Through the above linearization process, it can be clearly seen that the state of a given reference trajectory and control volume The error between the actual trajectory and the approximation process has a crucial impact on the accuracy of the approximation process. The specific process of applying the sequential convex optimization method in trajectory planning is to first use a certain initial trajectory as a reference trajectory to solve the convex optimization problem, and then use the optimal solution obtained this time as the reference trajectory for the next convex optimization solution, and iterate. This series of convex optimization sub-problems will converge to the final solution, which can be used as the solution to the original problem P1. The process can be described as follows:

[0136] 1) k represents the number of iterations. Assume k = 0. The initial trajectory is generated by the three-dimensional trajectory rapid generation method based on the maneuver coefficient according to the initial state constraints and the final position, height, and speed constraints. After processing, the first reference trajectory {x (0) ,u (0)}.

[0137] 2) When k ≥ 1, the state variable of the reference trajectory and control variables Substitute into P1 and find the solution to the problem as {x k ,u k}.

[0138] 3) Check whether the following sequence convergence conditions are met:

[0139] sup|x k -x k-1 |≤ε,k≥1

[0140] where x k is the state result of the kth iteration, x k-1 is the state quantity result of the k-1th iteration. ε is the tolerance threshold of sequence convergence. If the condition is met, go to step 4); otherwise, let k = k + 1 and repeat step 2).

[0141] 4) Get the optimal trajectory {x*,u*}={x k ,u k}.

[0142] All of the above x=[r,θ,φ,v,γ,ψ,σ,t] T is the state vector, u=[u t ,u σ ] T To control the amount.

[0143] The effectiveness of the method of the present invention is verified by simulation results.

[0144] The SOCP problem was established using MATLAB's modeling toolbox YALMIP and solved using the MOSEK software package. The simulation results were obtained on a desktop computer with an Intel-core i9-10900k 3.70GHz processor.

[0145] The simulation selected CAV-H as the object, and the aircraft parameters were set as follows: m = 907 kg, S A =0.484m 2 , the flight process constraints are n max =3g,q max =70kPa. The aircraft angle of attack profile is designed as a piecewise linear function of speed:

[0146]

[0147] The parameters α1 = 20°, α2 = 12°, v1 = 5000m / s, v2 = 2000m / s are selected. The lift coefficient C of the aircraft L and the drag coefficient C D Obtained by interpolation of aerodynamic data. Other basic constants: ρ0 = 1.752 kg / m 3 ,h s =6700m,K Q =9.4369×10 -5 .

[0148] The trust region and iteration termination conditions are set as:

[0149]

[0150]

[0151] The initial and final state constraints of the simulation are shown in Table 1, h0 * and h f * represents the altitude, and the limit on the change of the roll angle is σ max =80deg,u σ,max =10deg / s. After testing, the end time of the initial trajectory is t M =1502.55s, set the expected terminal time to 1480s, 1500s, and 1520s for simulation. Then select t f * = 1500s as an example to demonstrate its iterative process and compare it with the result obtained by pseudo-spectral method under the same conditions.

[0152] Table 1 Initial state and terminal state

[0153]

[0154] Figure 2 A schematic diagram of a curve showing changes in altitude, velocity, trajectory inclination angle and heading angle over time at three given terminal times provided in an embodiment of the present invention, wherein the horizontal axis is time (Time), and the vertical axes are respectively the altitude (Altitude), velocity (Velocity), trajectory inclination angle (Flight-Path-Angle) and heading angle (Heading-Angle) at three given terminal times (1480s, 1500s, 1520s). Figure 3 A schematic diagram of a bank angle command curve under three given terminal times provided in an embodiment of the present invention, wherein the horizontal axis is time (Time), and the vertical axis is the bank angle (BankAngle) command curve under three conditions. Figure 4 A schematic diagram of ground projection of flight trajectories at three given terminal times provided in an embodiment of the present invention, wherein the horizontal coordinate is longitude and the vertical coordinate is latitude. Figure 3 and Figure 4 The roll angle command curves and ground projections of the flight trajectory in the three cases are shown respectively. It can be seen that the flight time is precisely controlled and the terminal states are satisfied. And when the prescribed flight time becomes longer, the planned trajectory will increase the longitudinal maneuver to extend the flight time. The time for solving the convex optimization subproblem each time is between 0.5s and 1.3s. The number of iterations for these three optimizations are 6, 9, and 5 respectively, and the total optimization time is 4.926s, 7.865s, and 3.684s respectively.

[0155] The simulation continued by simulating the coordinated reentry of two CAV aircraft. f * = 1500s, the initial and final conditions of CAV1 refer to Table 1, CAV2 only changes the initial heading angle ψ0 * =59deg. Figure 5 A schematic diagram of a curve showing changes in altitude, speed, trajectory inclination and heading angle of two aircraft over time provided by an embodiment of the present invention, Figure 6 A schematic diagram of ground projection of the flight trajectories of two aircraft provided in an embodiment of the present invention. Figure 5 and Figure 6 The curves of the changes of various state quantities of the two aircraft over time and the ground projection of the trajectory during the coordinated reentry flight are described. It can be seen that at the end of the flight of the two aircraft, the total time and each state are consistent, realizing the coordinated reentry planning, which provides a methodological basis for the realization of the reentry formation of hypersonic aircraft.

[0156] Figure 7A schematic diagram of an optimization process curve of the objective function of two aircraft provided in an embodiment of the present invention, wherein the horizontal axis is the step number (Step Number) and the vertical axis is the value of the objective function (Value of Objective Function). Figure 8 A schematic diagram of the simulation results of the flight trajectories of two aircraft provided in an embodiment of the present invention, wherein Validation represents a validation curve. Figure 7 The optimization process of the objective function corresponding to the two aircraft is shown. In addition, in order to verify the rationality of this convexification method, the optimized control quantity results are substituted into the original dynamic equation numerical integration using the fourth-order Runge-Kutta method, with a simulation step length of 0.1s. The results are shown in Figure 8 It can be seen that the integral trajectory is very close to the optimization trajectory, which means that the approximate processing is more in line with reality.

[0157] In summary, the present invention proposes a multi-aircraft collaborative reentry trajectory planning method based on sequential convex optimization, which can plan the ballistic trajectories of multiple aircraft with the same reentry flight time under multiple constraints, thereby realizing multi-state collaborative reentry trajectory planning, improving the efficiency and accuracy of multi-aircraft collaborative reentry trajectory planning, and verifying the effectiveness of the proposed method through numerical simulation.

[0158] In addition, corresponding to the multi-aircraft cooperative reentry trajectory planning method provided above, the present invention also provides a multi-aircraft cooperative reentry trajectory planning system, see Fig. 9 , the multi-aircraft collaborative reentry trajectory planning system includes:

[0159] The aircraft modeling and model improvement module 901 is used to establish a dynamic model of the aircraft and improve the dynamic model by redefining independent variables to generate an improved dynamic model of the aircraft;

[0160] A trajectory planning problem model building module 902 is used to establish a terminal time constraint according to the improved aircraft dynamics model, and to add other constraints of the aircraft to determine the trajectory planning problem model;

[0161] A trajectory planning problem model processing module 903 is used to process the trajectory planning problem model to obtain a processed trajectory planning problem model;

[0162] An initial reference trajectory generating module 904, configured to generate a usable initial reference trajectory according to desired initial and terminal conditions;

[0163] The collaborative reentry trajectory solving module 905 is used to determine the collaborative reentry trajectory of multiple aircraft using a sequential convex optimization method according to the processed trajectory planning problem model and the initial reference trajectory.

[0164] The multi-aircraft collaborative re-entry trajectory planning system provided in an embodiment of the present invention has similar working principles and beneficial effects as the multi-aircraft collaborative re-entry trajectory planning method described in the above embodiment, so they will not be described in detail here. For specific contents, please refer to the introduction of the above method embodiment.

[0165] The present invention also provides an electronic device, which may include: a processor, a communication interface, a memory and a communication bus. The processor, the communication interface and the memory communicate with each other through the bus. The processor may call a computer program in the memory to execute the multi-aircraft cooperative reentry trajectory planning method.

[0166] In addition, when the computer program in the above-mentioned memory is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory, a random access memory, a magnetic disk or an optical disk.

[0167] Furthermore, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, and when the computer program is executed, the multi-aircraft collaborative re-entry trajectory planning method can be implemented.

[0168] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0169] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A multi-aircraft collaborative reentry trajectory planning method, characterized in that: include: Establishing a dynamic model of the aircraft, and improving the dynamic model by redefining independent variables to generate an improved dynamic model of the aircraft; The step of establishing a dynamic model of the aircraft and improving the dynamic model by redefining independent variables to generate an improved dynamic model of the aircraft specifically includes: A dynamic model of a hypersonic glide vehicle is established; the dynamic model uses a kinematic equation with time t as an independent variable to describe the unpowered glide process of the vehicle during reentry; By redefining the normalized time τ∈[0,1] as an independent variable, the dynamic model is improved to generate an improved aircraft dynamic model where x=[r,θ,φ,v,γ,ψ,σ,t] T is the flight state vector; r is the distance from the center of the earth to the aircraft, θ and φ represent longitude and latitude respectively, v is the flight speed of the aircraft relative to the earth, γ and ψ are the ballistic inclination angle and velocity heading angle respectively, and σ is the roll angle; u σ is the rate of change of the roll angle; time control quantity f(x,u σ ) and f Ω (x,u σ ) represent the terms without and with the earth's rotation angular velocity in the improved aircraft dynamics model, respectively; Establishing terminal time constraints according to the improved aircraft dynamics model, and adding other constraints of the aircraft to determine the trajectory planning problem model; Processing the trajectory planning problem model to obtain a processed trajectory planning problem model; Generate a usable initial reference trajectory based on desired initial and terminal conditions; According to the processed trajectory planning problem model and the initial reference trajectory, a sequential convex optimization method is used to determine the multi-aircraft cooperative reentry trajectory.

2. The multi-aircraft coordinated reentry trajectory planning method according to claim 1, characterized in that: The terminal time constraint is established according to the improved aircraft dynamics model, and other constraints of the aircraft are added to determine the trajectory planning problem model, specifically including: The terminal time constraint is established according to the improved aircraft dynamics model, and other constraints of the aircraft are added to determine the trajectory planning problem model. Where J represents the optimization function, represents the heat flux density; n max ,q max They are the heat flux densities that the aircraft can withstand. The dimensionless maximum values ​​of overload n and dynamic pressure q; g1-g3 represent the functional expressions of the constraints, K Q is the heat flux density constant, ρ is the atmospheric density, L and D are the lift and drag accelerations respectively; σ max is the limit value of the roll angle; u σmax is the limit value of the rate of change of the roll angle; is the expected total flight time; Respectively represent the initial state quantity; They represent the terminal state quantities respectively; v fmin , v fmax represent the minimum and maximum expected terminal velocities, respectively.

3. The multi-aircraft coordinated reentry trajectory planning method according to claim 2, characterized in that: The processing of the trajectory planning problem model to obtain a processed trajectory planning problem model specifically includes: Based on the small disturbance linearization method, the trajectory planning problem model is linearized and convexified, and the trajectory planning problem model P0 is converted into a continuous convex optimization problem model P1; The continuous convex optimization problem model P1 is discretized to obtain a processed trajectory planning problem model P2.

4. The multi-aircraft coordinated reentry trajectory planning method according to claim 3 is characterized in that: The generating of an available initial reference trajectory according to the desired initial and terminal conditions specifically includes: Determine the initial sequence of control variables based on the desired initial and terminal conditions in and They represent the roll angle change rate control amount and time control amount of discrete point i respectively; The initial sequence of control variables is substituted into the trajectory planning problem model P0, and a usable initial reference trajectory is generated through fourth-order Runge-Kutta numerical integration.

5. A multi-aircraft collaborative reentry trajectory planning system, characterized in that: include: The aircraft modeling and model improvement module is used to establish a dynamic model of the aircraft and improve the dynamic model by redefining independent variables to generate an improved aircraft dynamic model; The step of establishing a dynamic model of the aircraft and improving the dynamic model by redefining independent variables to generate an improved dynamic model of the aircraft specifically includes: A dynamic model of a hypersonic glide vehicle is established; the dynamic model uses a kinematic equation with time t as an independent variable to describe the unpowered glide process of the vehicle during reentry; By redefining the normalized time τ∈[0,1] as an independent variable, the dynamic model is improved to generate an improved aircraft dynamic model where x=[r,θ,φ,v,γ,ψ,σ,t] T is the flight state vector; r is the distance from the center of the earth to the aircraft, θ and φ represent longitude and latitude respectively, v is the flight speed of the aircraft relative to the earth, γ and ψ are the ballistic inclination angle and velocity heading angle respectively, and σ is the roll angle; u σ is the rate of change of the roll angle; time control quantity f(x,u σ ) and f Ω (x,u σ ) represent the terms without and with the earth's rotation angular velocity in the improved aircraft dynamics model, respectively; A trajectory planning problem model building module is used to establish a terminal time constraint according to the improved aircraft dynamics model, and to add other constraints of the aircraft to determine the trajectory planning problem model; A trajectory planning problem model processing module, used to process the trajectory planning problem model to obtain a processed trajectory planning problem model; An initial reference trajectory generation module, used to generate a usable initial reference trajectory according to desired initial and terminal conditions; The collaborative reentry trajectory solving module is used to determine the collaborative reentry trajectory of multiple aircraft using a sequential convex optimization method based on the processed trajectory planning problem model and the initial reference trajectory.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the multi-aircraft collaborative re-entry trajectory planning method according to any one of claims 1 to 4 is implemented.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed, the multi-aircraft collaborative re-entry trajectory planning method according to any one of claims 1 to 4 is implemented.

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