CN115268501A - Multi-aircraft collaborative reentry trajectory planning method, system, electronic device and medium - Google Patents
Multi-aircraft collaborative reentry trajectory planning method, system, electronic device and medium Download PDFInfo
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Abstract
The invention relates to a method, a system, electronic equipment and a medium for planning a multi-aircraft collaborative reentry trajectory, and belongs to the field of aircraft trajectory planning. Firstly, establishing a dynamic model of an aircraft, and improving the dynamic model by redefining independent variables; establishing terminal time constraints according to the improved aircraft dynamics model, and adding other constraints of the aircraft to determine and process a trajectory planning problem model to obtain a processed trajectory planning problem model; and generating an available initial reference track according to expected initial and terminal conditions, and determining the multi-aircraft cooperative reentry track by adopting a sequence convex optimization method in combination with the processed track planning problem model. The method can solve the problem of planning the collaborative reentry trajectory of the multi-hypersonic gliding aircraft, and improve the efficiency and the precision of planning the collaborative reentry trajectory of the multi-hypersonic gliding aircraft.
Description
Technical Field
The invention relates to the technical field of aircraft trajectory planning, in particular to a method, a system, electronic equipment and a medium for planning a multi-aircraft collaborative reentry trajectory.
Background
The Hypersonic Glide Vehicle (HGV) is a near space vehicle, has the capabilities of high speed, large-scale maneuvering and long-distance gliding, has the characteristics of wide combat range, strong defense capability and the like, and has wide application prospect. In order to combat the missile defense system, it is necessary to increase the penetration capacity of the HGV. However, with the development of an air defense weapon system, the defense and interception capabilities of a single hypersonic aircraft are stronger and stronger at present, and the striking effect of the hypersonic aircraft is greatly limited. Under such a background, it becomes more necessary to develop a cooperative combat technology for a plurality of hypersonic aircrafts. The interception difficulty of a defense system can be greatly increased by the cooperative combat attack of multiple aircrafts, and the saturation attack on the target is realized. And for control objects such as a hypersonic glide vehicle with large flight environment uncertainty, severe time-varying parameters and serious coupling, trajectory planning and tracking control under the multi-constraint cooperative attack condition are more challenging.
The research on the trajectory planning of the reentry section of the hypersonic flight vehicle is a nonlinear planning problem with complex multi-constraint limits. In early studies, planning the state profile of a trajectory was a common method and achieved many results with continuous improvement. Notably, real-time performance is crucial in HGV co-track optimization. The convex optimization method has good convergence performance and wide applicability, and is widely applied to the field of track optimization. Trajectory optimization problems with complex constraints and non-linear dynamics can be transformed into a series of convex optimization problems by convex techniques.
Research on the problem of cooperative reentry guidance of multi-hypersonic aircraft has mostly focused on achieving temporal cooperation of the reentry segment. The main method at present is to analyze and design the corresponding relation between the flight time of the reentry stage and each state quantity, and correct the flight trajectory to realize the expected time coordination. But it cannot directly control the end time, wasting the number of solutions. And the target function aims at ensuring terminal constraint and cannot meet better performance indexes such as minimum heat flow overload and the like. Therefore, the problem of collaborative reentry trajectory optimization for multiple aircraft requires further attention and research.
Disclosure of Invention
In order to solve or at least alleviate the above problems, the invention provides a method, a system, an electronic device and a medium for planning a multi-aircraft collaborative reentry trajectory, so as to improve efficiency and precision of planning the multi-aircraft collaborative reentry trajectory.
In order to achieve the purpose, the invention provides the following scheme:
in one aspect, the invention provides a method for planning a multi-aircraft collaborative reentry trajectory, which comprises the following steps:
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;
establishing terminal time constraints according to the improved aircraft dynamics model, and determining a trajectory planning problem model by adding other constraints of the aircraft;
processing the track planning problem model to obtain a processed track planning problem model;
generating an available initial reference trajectory according to desired initial and terminal conditions;
and determining the multi-aircraft cooperative reentry trajectory by adopting a sequence convex optimization method according to the processed trajectory planning problem model and the initial reference trajectory.
Optionally, the establishing a dynamic model of the hypersonic glide vehicle, and modifying the dynamic model by redefining the independent variables to generate a modified dynamic model of the vehicle specifically includes:
establishing a dynamic model of the hypersonic glide aircraft; the dynamic model adopts a kinematics equation with time t as an independent variable to describe the unpowered gliding process of the reentry section of the aircraft;
by redefining normalized time tau epsilon 0,1]Modifying the dynamics model for independent variables to generate a modified aircraft dynamics model
Wherein x = [ r, theta, phi, v, gamma, psi, sigma, t] T Is a flight state vector; r is the distance from the geocenter to the aircraft, θ and φ represent longitude and latitude, respectively, v is the flight velocity of the aircraft relative to the earth, γ and ψ are the ballistic inclination angle and the velocity heading angle, respectively, and σ is the roll angle; u. of σ Is the rate of change of roll angle; amount of time control
f(x,u σ ) And f Ω (x,u σ ) Terms representing no and with earth rotation angular velocities in the improved aircraft dynamics model, respectively.
Optionally, the establishing a terminal time constraint according to the improved aircraft dynamics model, and determining a trajectory planning problem model by adding other constraints of the aircraft specifically include:
establishing terminal time constraint according to the improved aircraft dynamics model, and determining a trajectory planning problem model P0 by adding other constraints of the aircraft
Wherein J is an expression of an optimization function,
representing the heat flow density;
respectively the heat flux density that the aircraft can withstand
Non-dimensionalized maximum values of overload n and dynamic pressure q; g is a radical of formula 1 -g 3 Functional expression representing a constraint, K Q Is the heat flux density constant, ρ is the atmospheric density, and L and D are the lift and drag accelerations, respectively; sigma max Is the clipping value of the roll angle; u. of σmax Is the clipping value of the roll angle rate of change;
is the desired total time of flight; r is 0 ,θ 0 ,φ 0 ,v 0 ,γ 0 ,ψ 0 Respectively representing initial state quantities; r is f ,θ f ,φ f ,v f ,γ f ,ψ f Respectively representing terminals a time state quantity; v. of fmin ，v fmax Respectively representing the minimum and maximum values of the desired terminal speed.
Optionally, the processing the trajectory planning problem model to obtain a processed trajectory planning problem model specifically includes:
carrying out linearization processing and convexity processing on the track planning problem model based on a small disturbance linearization method, and converting the track planning problem model P0 into a continuous convex optimization problem model P1;
and carrying out discretization processing on the continuous convex optimization problem model P1 to obtain a processed trajectory planning problem model P2.
Optionally, the generating an available initial reference trajectory according to the desired initial and terminal conditions specifically includes:
determining an initial sequence of control quantities based on desired initial and terminal conditions
Wherein
And
respectively representing the roll angle change rate control amount and the time control amount of the i discrete points;
and substituting the control quantity initial sequence into the trajectory planning problem model P0, and generating an available initial reference trajectory through fourth-order Runge-Kutta numerical integration.
In another aspect, the present invention further provides a system for planning a reentry trajectory in cooperation with multiple aircrafts, including:
the aircraft modeling and model improving module is used for establishing a dynamic model of the aircraft, improving the dynamic model by redefining independent variables and generating an improved dynamic model of the aircraft;
the trajectory planning problem model building module is used for building a terminal time constraint according to the improved aircraft dynamics model and determining a trajectory planning problem model by adding other constraints of the aircraft;
the trajectory planning problem model processing module is used for processing the trajectory planning problem model to obtain a processed trajectory planning problem model;
an initial reference track generation module for generating an available initial reference track according to desired initial and terminal conditions;
and the cooperative reentry trajectory solving module is used for determining the cooperative reentry trajectory of the multiple aircrafts by adopting a sequence convex optimization method according to the processed trajectory planning problem model and the initial reference trajectory.
In another aspect, the present invention further provides an electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor implements the method for planning multiple aircraft collaborative reentry trajectories when executing the computer program.
In another aspect, the present invention further provides a non-transitory computer-readable storage medium, on which a computer program is stored, and the computer program, when executed, implements the multi-aircraft collaborative reentry trajectory planning method.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a method, a system, electronic equipment and a medium for planning a multi-aircraft collaborative reentry trajectory, wherein the method comprises the following steps: 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; establishing terminal time constraints according to the improved aircraft dynamics model, and determining a trajectory planning problem model by adding other constraints of the aircraft; processing the track planning problem model to obtain a processed track planning problem model; generating an available initial reference trajectory according to desired initial and terminal conditions; and determining the multi-aircraft cooperative reentry trajectory by adopting a sequence convex optimization method according to the processed trajectory planning problem model and the initial reference trajectory. According to the method, the dynamics model is improved by redefining the independent variables, and the improved aircraft dynamics model can directly control the tail end time, so that the planning efficiency of the multi-aircraft collaborative reentry trajectory can be improved; the track planning problem model determined by the method selects the minimum heat flux overload as the optimized objective function, and can meet better performance indexes such as the minimum heat flux overload and the like, so that the planning precision of the multi-aircraft collaborative reentry track is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
Fig. 1 is a flowchart of a method for planning a multiple-aircraft collaborative reentry trajectory according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the time-dependent changes in altitude, speed, ballistic inclination and course angle for three given terminals according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a roll angle command curve at three given terminal times according to an embodiment of the present invention;
FIG. 4 is a schematic ground projection of flight paths at three given terminal times according to an embodiment of the present invention;
FIG. 5 is a schematic view of the variation of altitude, speed, ballistic inclination and course angle of two aircraft over time according to an embodiment of the present invention;
FIG. 6 is a schematic ground projection of flight trajectories of two aircraft according to an embodiment of the present invention;
FIG. 7 is a graph illustrating an optimization process of an objective function of two aircraft according to an embodiment of the present invention;
FIG. 8 is a schematic diagram of a simulation result of flight trajectories of two aircrafts according to an embodiment of the present invention;
fig. 9 is a schematic structural diagram of a multiple aircraft collaborative reentry trajectory planning system according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The invention aims to provide a method, a system, electronic equipment and a medium for planning a multi-aircraft collaborative reentry trajectory, which can solve the problem of planning the collaborative reentry trajectory of a plurality of hypersonic glide aircrafts and improve the efficiency and the precision of planning the multi-aircraft collaborative reentry trajectory.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of a method for planning a multiple-aircraft collaborative reentry trajectory according to an embodiment of the present invention. Referring to fig. 1, the method for planning the collaborative reentry trajectory of multiple aircraft according to the present invention includes:
step 101: and establishing a dynamic model of the aircraft, and modifying the dynamic model by redefining independent variables to generate the modified dynamic model of the aircraft.
Firstly, establishing a classic hypersonic gliding aircraft (aircraft for short) reentry dynamic equation as a dynamic model of the aircraft, and then improving the original equation in order to realize free and controllable terminal time, thereby generating an improved dynamic model of the aircraft.
The step 101 of establishing a dynamic model of the hypersonic glide aircraft, and modifying the dynamic model by redefining an independent variable to generate a modified aircraft dynamic model specifically includes:
step 1.1: establishing a dynamic model of the hypersonic glide aircraft, wherein the dynamic model adopts a kinematics equation with time t as an independent variable to describe an unpowered glide process of the aircraft at a reentry section; assuming that the earth is a sphere and the rotation of the sphere is considered, the dimensionless equation of the dynamic model is as follows:
dr/dt＝vsinγ
dθ/dt＝vcosγsinψ/(rcosφ)
dφ/dt＝vcosγcosψ/r
dv/dt＝-D-sinγ/r 2 +Ω 2 rcosφ(sinγcosφ-cosγsinφcosψ)
dγ/dt＝[Lcosσ-cosγ/r 2 +v 2 cosγ/r+2Ωvcosφsinψ+Ω 2 rcosφ(cosγcosφ+sinγsinφcosψ)]/v
dψ/dt＝[Lsinσ/cosγ+v 2 cosγsinψtanφ/r-2Ωv(tanγcosφcosψ-sinφ)+Ω 2 rsinφcosφsinψ/cosγ]/v
dσ/dt＝u σ
the distance R from the earth's center to the aircraft in the equation is given by the mean radius R of the earth 0 =6378140m dimensionless. The state quantities θ and φ are longitude and latitude, respectively. v is the flight velocity relative to the earth, is
Dimensionless, g 0 ＝9.807m/s 2 Is the gravitational acceleration of the earth's surface. γ, ψ are the ballistic inclination angle and the velocity heading angle, respectively. The constant Ω is the rotational angular velocity of the earth, which is
And (4) dimensionless. Time t of independent variable
And (4) dimensionless. σ is the roll angle, in order to ensure flightStability of the line, selecting rate of change u of roll angle σ As a control quantity, it is
And (4) dimensionless. L and D are each g 0 Nondimensionalized lift and drag accelerations, respectively, specifically represented as:
where m is the dimensional aircraft mass, and the atmospheric density ρ = ρ 0 exp(-h/h s ) Is a function of the altitude of flight, where h s ＝7200m，S A For aircraft reference area, C L 、C D Respectively, the lift coefficient and drag coefficient of the aircraft, which are related to the angle of attack and mach number of the aircraft. The invention designs the angle of attack-velocity profile as a commonly used piecewise function.
Step 1.2: by redefining normalized time tau epsilon 0,1]The dynamic model is improved for independent variables, and an improved aircraft dynamic model is generated
Wherein x = [ r, theta, phi, v, gamma, psi, sigma, t] T Is a flight state vector; r is the distance from the geocenter to the aircraft, θ and φ represent longitude and latitude, respectively, v is the flight velocity of the aircraft relative to the earth, γ and ψ are the ballistic inclination angle and the velocity heading angle, respectively, and σ is the roll angle; u. of σ Is the rate of change of roll angle; amount of time control
f(x,u σ ) And f Ω (x,u σ ) Terms representing no and earth rotation angular velocities in the improved aircraft dynamics model, respectively.
The present invention improves the dynamic model of an aircraft by redefining the independent variables. Suppose that the initial and final time during the flight are t 0 And t f Redefining normalized time tau epsilon [0,1 ∈ ]]For the independent variable, the time interval of the original equation is mapped to [0,1 ]]And introducing a time control quantity u t ＝t f -t 0 Thus, the actual dimensionless time t can be expressed as:
t＝t 0 +(t f -t 0 )τ,τ∈[0,1]
then, the original argument dimensionless time t is used as a new state quantity, and the differential equation with respect to the normalized time τ is obtained as:
now let the flight state vector be x = [ r, θ, φ, v, γ, ψ, σ, t] T By separating the terms with the rotational angular velocity of the earth, the system of kinetic differential equations can be written as follows:
wherein, f (x, u) σ ) Representing the part without angular velocity of rotation of the earth, f Ω (x,u σ ) Representing the portion with rotational angular velocity of the earth and being defined by f 1 -f 6 And f Ω4 -f Ω6 Representing the terms in each equation. Then, the above equation is used to obtain the motion equation with τ as the independent variable as the improved dynamic model of the aircraft, which can be expressed as:
wherein u is t The new time control quantity is added.
Step 102: and establishing terminal time constraint according to the improved aircraft dynamics model, and determining a trajectory planning problem model by adding other constraints of the aircraft.
The classical aircraft reentry path constraint may be expressed as:
wherein
Respectively, the heat flux density that the aircraft can withstand
The non-dimensionalized maximum values of overload n and dynamic pressure q. g is a radical of formula 1 -g 3 Functional expression representing a constraint, K Q Is the heat flow density constant, ρ is the atmospheric density, and L and D are the lift and drag accelerations, respectively.
To precisely meet the cooperative constraint of total reentry time of flight, the control quantity u t Needs to be set to the desired time of flight and maintained throughout. At the same time, the roll angle of the aircraft and its rate of change should be limited to a certain range to ensure stability of the aircraft attitude.
Where σ is the roll angle, σ max Is the clipping value of the roll angle; selecting the rate of change u of the roll angle σ As a control amount, u σmax Is the clipping value of the roll angle rate of change; u. of t Is a time control quantity which is a quantity of time control,
is the desired total time of flight.
The optimization process limits the initial and final states of the reentry stage of the hypersonic gliding aircraft, and mainly aims at the height, longitude and latitude, speed, trajectory inclination angle and course angle of the hypersonic gliding aircraft to realize multi-state collaborative planning.
Wherein r is 0 ,θ 0 ,φ 0 ,v 0 ,γ 0 ,ψ 0 Respectively represent initial state quantities, r f ,θ f ,φ f ,v f ,γ f ,ψ f Respectively, represent the terminal time state quantities. v. of fmin ，v fmax Respectively representing the minimum and maximum values of the desired terminal speed.
The invention selects the minimum heat flow overload as an optimized objective function, combines the equation and inequality constraint, and can describe the collaborative reentry trajectory planning with flight time constraint as the following non-convex optimal control problem:
P0
subject to:
in the formula, J represents an optimization function,
indicating the heat flow density. The state vector is x = [ r, theta, phi, v, gamma, psi, sigma, t] T The controlled variable is [ u ] t ,u σ ] T τ is normalized time, f (x, u) σ ) And f Ω (x,u σ ) Is the dynamic equation of the system and is,
respectively the heat flux density that the aircraft can withstand
The non-dimensionalized maximum values of overload n and dynamic pressure q. g is a radical of formula 1 -g 3 Functional expression representing a constraint, K Q Is the heat flow density constant, ρ is the atmospheric density, and L and D are the lift and drag accelerations, respectively. R is the distance from the geocentric to the aircraft and the state quantities θ and φ are the longitude and latitude, respectively. v is the speed of flight relative to the earthDegrees, γ, ψ are the ballistic inclination angle and the velocity heading angle, respectively. The constant Ω is the rotational angular velocity of the earth, σ is the roll angle, σ max Is the limiting value of the roll angle; rate of change u of roll angle σ As a control quantity, u σmax Is the clipping value of the roll angle rate of change; u. of t Is a time control quantity which is a quantity of time control,
is the desired total time of flight. r is 0 ,θ 0 ,φ 0 ,v 0 ,γ 0 ,ψ 0 Respectively represent initial state quantities, r f ,θ f ,φ f ,v f ,γ f ,ψ f Respectively, represent the terminal time state quantities. v. of fmin ，v fmax Respectively representing the minimum and maximum values of the desired terminal speed. P0 is the determined trajectory planning problem model.
Step 103: and processing the track planning problem model to obtain a processed track planning problem model.
The trajectory planning problem model P0 determined in step 102 is a highly nonlinear optimal control problem, and in step 103, approximation processing is performed on a non-convex expression based on a small disturbance linearization method; and then discretizing to convert the finite-dimension second-order cone problem into a finite-dimension second-order cone problem which can be solved by a sequence convex optimization method.
The step 103 of processing the trajectory planning problem model to obtain a processed trajectory planning problem model specifically includes:
step 3.1: carrying out linearization processing and convexity processing on the track planning problem model based on a small disturbance linearization method, and converting the track planning problem model P0 into a continuous convex optimization problem model P1;
the kinetic equations, process constraints and optimization objective functions are all in a non-convex form. Given a fixed historical state
They can be linearized by a first order taylor expansion at this point according to the theory of small perturbation linearization.
In the equation of motion, the controlled variable is coupled with the state quantity. Therefore, a first order taylor expansion of the multivariate function is needed for linearization. With F (x, u) and F Ω (x, u) to represent the terms without and with the earth's rotational angular velocity, respectively, in the kinetic equation, due to F Ω (x is, the value of the u) portion is relatively small, it can be approximated directly with a fixed reference state:
the result of the linearization of the kinetic equation is then:
wherein
Nonlinear path constraint g j (r, v) are functions related to the earth's center distance r and velocity v, and can be related to a given state by
Linearization:
wherein
In addition, in order to reduce approximation errors as much as possible and ensure that the optimized variables take values near a given reference point, a trust domain constraint is introduced, where δ is the size of the trust domain:
the integral type objective function can also be linearized with reference to the above equation. After processing, the trajectory planning problem model P0 is converted into a continuous convex optimization problem model P1.
P1:
subject to:
In the formula, J represents an optimization function,
indicating the heat flow density. The state vector is x = [ r, theta, phi, v, gamma, psi, sigma, t] T The controlled variable is u = [ u ] t ,u σ ] T τ is normalized time, using F (x, u) and F Ω (x, u) to represent the terms without and with the earth rotation angular velocity, respectively, in the kinetic equation,
g 1 -g 3 a functional expression representing a constraint is represented by,
r is the distance from the geocentric to the aircraft, and the state quantities θ and φ are the longitude and latitude, respectively. v is the flight velocity relative to the earth, and γ, ψ are the ballistic inclination angle and the velocity heading angle, respectively. σ is the roll angle, σ max Is the clipping value of the roll angle; rate of change u of roll angle σ As a control quantity, u σmax Is the clipping value for the roll angle rate of change; u. of t Is a time control quantity which is a quantity of time control,
is the desired total time of flight. r is 0 ,θ 0 ,φ 0 ,v 0 ,γ 0 ,ψ 0 Respectively represent initial state quantities, r f ,θ f ,φ f ,v f ,γ f ,ψ f Respectively, representing the terminal time state quantities. v. of fmin ，v fmax Respectively representing the minimum and maximum values of the desired terminal speed.
Representing the reference state of the state vector x, δ being the size of the trust domain.
Step 3.2: and carrying out discretization processing on the continuous convex optimization problem model P1 to obtain a processed trajectory planning problem model P2.
In order to obtain a numerical solution of the continuous optimal control problem P1, it is necessary to perform discretization processing on it. The invention adopts a trapezoidal discretization method, firstly, a normalized time domain is divided into N equal intervals to generate N +1 independent variable nodes, and the step length of each section is delta tau =1/N. All discrete argument nodes are denoted as { τ } 0 ,τ 1 ,τ 2 ,...,τ N In which τ is i ＝τ i-1 + Δ τ, i =1,2. Then the state quantity and control quantity corresponding to each node are discretized into a sequence x 0 ,x 1 ,x 2 ,...,x N And { u } 0 ,u 1 ,u 2 ,...,u N }. Based on the above sequence, the kinetic equation can be numerically integrated as follows:
wherein, k represents the iteration times, and the last iteration result is used as the reference state of the solution, namely
Δ τ is the discrete step size, and the state vector is x = [ r, θ, φ, v, γ, ψ,σ,t] T The controlled variable is u = [ u ] t ,u σ ] T Tau is normalized time, using F (x, u) and F Ω (x, u) to represent the terms without and with, respectively, the earth's rotational angular velocity in the kinetic equation,
meanwhile, other constraints are also discretized respectively and can be expressed as:
where variables with a k-1 superscript are all indicated in the last iteration and are used herein as reference values. g 1 -g 3 A functional expression representing a constraint is represented by,
σ is the roll angle, σ max Is the limiting value of the roll angle; rate of change u of roll angle σ As a control amount, u σmax Is the clipping value of the roll angle rate of change; u. of t Is a time control quantity which is a quantity of time control,
is the desired total time of flight. r is the distance from the earth's center to the aircraft, v is the flight velocity relative to the earth,
representing the reference state of the state vector x, δ being the size of the trust domain.
The heat flow load Q generated by accumulation with time in the flight process is also integrated by adopting a trapezoidal method:
where Δ τ is the discrete step size, Q i Is the heat flow load at each discrete point, g 1 (r, v) represents the process constraint equation for heat flow density, r being the distance from the geocenter to the aircraft, v being the flight velocity relative to the earth.
P1 is then described as a discrete convex optimization sub-problem, resulting in a processed trajectory planning problem model P2:
P2
subject to:
wherein J represents an optimization function, Q N Is the heat flow load at the nth discrete point, i represents the serial number of the discrete point, and the state vector is x = [ r, θ, φ, v, γ, ψ, σ, t] T The controlled variable is u = [ u ] t ,u σ ] T And, delta tau is a discrete step size,
tau is normalized time, using F (x, u) and F Ω (x, u) to represent the terms without and with the earth rotation angular velocity, respectively, in the kinetic equation,
g 1 -g 3 a functional expression representing a constraint is represented by,
σ is inclinationSide angle, σ max Is the clipping value of the roll angle; rate of change u of roll angle σ As a control quantity, u σmax Is the clipping value of the roll angle rate of change; u. u t Is a time control quantity which is a quantity of time control,
is the desired total time of flight. r is the distance from the earth's center to the aircraft, v is the flying speed relative to the earth, the state quantities θ and φ are the longitude and latitude, respectively, and γ and ψ are the ballistic inclination angle and the velocity heading angle, respectively. r is 0 ,θ 0 ,φ 0 ,v 0 ,γ 0 ,ψ 0 Respectively represent initial state quantities, r f ,θ f ,φ f ,v f ,γ f ,ψ f Respectively, represent the terminal time state quantities. v. of fmin ，v fmax Respectively representing the minimum and maximum values of the desired terminal speed. x is the number of k-1 Representing the reference state of the state vector x and δ being the size of the trust domain.
Step 104: an available initial reference trajectory is generated based on desired initial and terminal conditions.
The step 104 of generating an available initial reference trajectory according to the desired initial and terminal conditions specifically includes:
step 4.1: determining an initial sequence of control quantities based on desired initial and terminal conditions
Wherein
And
the roll angle change rate control amount and the time control amount of the i discrete points are respectively represented.
The planning method of the initial trajectory uses energy as independent variable, defines the concept of maneuver coefficient to describe the coupling relation of the transverse and longitudinal trajectories, and then adjusts the direction angle deviation corridor in the transverse and lateral directions and controls the roll angle reversal to realize the desired lateral maneuver. However, the state set at this time does not include the flight time, and therefore, the time corresponding to each node in the trajectory is obtained according to the following formula according to the aircraft dynamics model. Note that this trace of numerical integration includes M +1 corresponding energy nodes.
Where i =0,1,.. M denotes the number of each discrete point, the subscripts i and i +1 denote the state quantities at that moment, { t } and 0 ,t 1 ,...,t M denotes a time series, r is a distance from the earth's center to the aircraft, v is a flying speed with respect to the earth, and γ is a ballistic inclination angle.
Then the obtained time series t 0 ,t 1 ,...,t M And the corresponding roll angle sequence [ sigma ] 0 ,σ 1 ,...,σ M Perform linear interpolation at equal time intervals. Thus, a sequence of roll angle states corresponding to the arrangement of equal time intervals can be obtained
The terminal time of flight of the initial trajectory is t M And solving for the expected terminal time t of the process f * Can be at t M But not too large adjustment, so as to avoid conflict between the initial trajectory and other constraints, and make iterative solution fail. Note that due to the limitation of the initial trajectory generation method, the terminal state thereof may have a certain difference from the expected terminal state, but within the allowable range, for the same reason. The initial sequence of the control quantity can be determined according to the terminal state constraint
Then, taking into account the clipping constraint, an initial sequence of the roll angle rate of change is found:
wherein the content of the first and second substances,
is a roll angle state sequence element, u, arranged corresponding to equal time intervals t,i Is the amount of time control at the discrete point of i,
represents the roll angle change rate control quantity of i discrete points and is used as an initial iteration track, and delta tau represents a time discrete step.
Step 4.2: and substituting the control quantity initial sequence into the track planning problem model P0, and generating an available initial reference track through fourth-order Runge-Kuta numerical integration.
Initial sequence of control quantity obtained in step 4.1
Substituting into the kinetic equation, and obtaining the state quantity sequence x of the initial trajectory corresponding to the equation again through the fourth-order Runge-Kutta numerical integration (0) As an initial reference track available. Note that the above variables all need to be dimensionless in advance.
Step 105: and determining the multi-aircraft cooperative reentry trajectory by adopting a sequence convex optimization method according to the processed trajectory planning problem model and the initial reference trajectory.
The solution process for the sequence convex optimization is described next.
By the above linearization processing, it is possible to clarify the state of a given reference trajectory
And control amount
The error from the true trajectory has a crucial influence on the accuracy of the approximation process. The specific process of the sequence convex optimization method applied to the trajectory planning is that firstly, a certain initial trajectory is taken as a reference trajectory to solve a convex optimization problemAnd taking the optimal solution obtained this time as a reference track of the next convex optimization solution, and performing iteration. The series of convex optimization sub-problems converge to the final solution, which can be used as the solution of the original problem P1, and the process can be described as follows:
1) The number of iterations is denoted by k. And setting k =0, and generating an initial track according to an initial state constraint and a final position, height and speed constraint by a three-dimensional track rapid generation method based on a maneuvering coefficient. Obtaining a first reference track { x after processing (0) ,u (0) }。
2) When k is more than or equal to 1, referring to the state variable of the track
And a control variable
Substituted into P1, and the solution of the problem is found to be { x k ,u k }。
3) The following sequence convergence conditions were examined:
sup|x k -x k-1 |≤ε,k≥1
wherein x is k Is the state quantity result of the kth iteration, x k-1 Is the state quantity result of the (k-1) th iteration. ε is the tolerance threshold for sequence convergence. If the condition is met, turning to the step 4); otherwise, let k = k +1, repeat step 2).
4) Obtaining the optimal track { x, u } = { x } k ,u k }。
All the foregoing x = [ r, θ, φ, v, γ, ψ, σ, t] T Is a state vector, u = [) t ,u σ ] T Is a control quantity.
The effectiveness of the method of the invention is verified by using the simulation result.
The SOCP problem was established using the MATLAB modeling toolkit YALMIP and solved using the MOSEK software package. Simulation results are obtained on a desktop computer adopting an Intel-core i9-10900k 3.70GHz processor.
CAV-H is selected as an object for simulation, and parameters of the aircraft are set as follows:m＝907kg，S A ＝0.484m 2 the flight process constraint is defined as
n max ＝3g，q max =70kPa. The aircraft angle of attack profile is designed as a piecewise linear function of velocity:
wherein a parameter alpha is selected 1 ＝20°，α 2 ＝12°，v 1 ＝5000m/s，v 2 =2000m/s. Coefficient of lift C of aircraft L And coefficient of resistance C D And the pneumatic data are interpolated. Other basic constants: rho 0 ＝1.752kg/m 3 ，h s ＝6700m，K Q ＝9.4369×10 -5 。
The trust domain and iteration termination condition are set to:
the simulation initial and final state constraints are shown in a table 1,h 0 * And h f * The limit to the change in the roll angle, expressed as altitude, is σ max ＝80deg，u σ,max =10deg/s. After testing, the end time t of the initial trajectory M =1502.55s, and the simulation was performed by setting the expected end times to 1480s, 1500s, and 1520s, respectively. Then select t f * And =1500s as an example, showing an iterative process and comparing with a result obtained by solving by adopting a pseudo-spectrum method under the same condition.
TABLE 1 initial and terminal states
Fig. 2 is a schematic diagram of the variation curves of Altitude, speed, trajectory inclination Angle and course Angle with Time at three given terminal times according to an embodiment of the present invention, where the abscissa is Time (Time) and the ordinate is Altitude (Altitude), speed (Velocity), trajectory inclination Angle (Flight-Path-Angle) and course Angle (Heading-Angle) at three given terminal times (1480 s, 1500s and 1520 s). Fig. 3 is a schematic diagram of a tilt angle command curve at three given terminal times according to an embodiment of the present invention, where the abscissa is Time (Time) and the ordinate is a tilt angle command curve in three cases. Fig. 4 is a schematic ground projection diagram of flight trajectories at three given terminal times, where the abscissa is Longitude (Longitude) and the ordinate is Latitude (Latitude), according to an embodiment of the present invention. Fig. 3 and 4 show the ground projection of the roll angle command curve and the flight trajectory in three cases, respectively, and it can be seen that the flight time is precisely controlled and the state of each terminal is satisfied. And when the specified flight time is longer, the planned trajectory will increase the longitudinal maneuver to extend the flight time. The time for solving the convex optimization subproblem is 0.5s to 1.3s, the iteration times of the three times of optimization are 6 times, 9 times and 5 times respectively, and the total optimization time is 4.926s, 7.865s and 3.684s respectively.
The simulation continues to simulate the situation of the cooperative reentry of two CAV aircrafts. Stipulate t f * Initial and final conditions of =1500s, CAV1 referring to Table 1, CAV2 compares to change only the initial heading angle ψ 0 * =59deg. Fig. 5 is a schematic diagram of the variation curves of the altitude, the speed, the ballistic inclination angle and the heading angle of two aircrafts with time according to the embodiment of the invention, and fig. 6 is a schematic diagram of the ground projection of the flight tracks of the two aircrafts according to the embodiment of the invention. Fig. 5 and fig. 6 describe the time-varying curves of the state quantities of the two aircrafts during the cooperative reentry flight and the ground projection of the trajectory, and it can be seen that at the flight ends of the two aircrafts, the total time and the states are consistent, and the cooperative reentry planning is realized, which provides a method basis for the realization of the formation of the reentry segments of the hypersonic aircrafts.
Fig. 7 is a schematic diagram of an optimization process curve of an objective Function of two aircraft according to an embodiment of the present invention, where the abscissa is the Step Number (Step Number) and the ordinate is the Value of the objective Function (Value of objective Function). Fig. 8 is a schematic diagram of a simulation result of flight trajectories of two aircraft according to an embodiment of the present invention, wherein Validation represents a verification curve. Fig. 7 shows the optimization process of the objective function corresponding to the two aircrafts. In addition, in order to verify the rationality of the present convex method, the optimized controlled variable result is substituted into the numerical integration of the original kinetic equation by using a four-step Runge Kutta method, the simulation step length is 0.1s, and the result is shown in FIG. 8. It can be seen that the integrated trajectory is very close to the optimized trajectory, indicating that the approximation process is more realistic.
In summary, the method for planning the reentry trajectory of the multi-aircraft based on the sequence convex optimization can plan the trajectory with the same reentry flight time of the multi-aircraft under the multi-constraint condition, so that the reentry trajectory planning of multi-state cooperation is realized, the efficiency and the precision of the planning of the reentry trajectory of the multi-aircraft cooperation are improved, and the effectiveness of the method is verified through numerical simulation.
In addition, corresponding to the above provided multi-aircraft collaborative reentry trajectory planning method, the present invention further provides a multi-aircraft collaborative reentry trajectory planning system, referring to fig. 9, the multi-aircraft collaborative reentry trajectory planning system includes:
an aircraft modeling and model improving module 901, configured to establish a dynamic model of an aircraft, and improve the dynamic model by redefining an independent variable to generate an improved dynamic model of the aircraft;
a trajectory planning problem model establishing module 902, configured to establish a terminal time constraint according to the improved aircraft dynamics model, and determine a trajectory planning problem model by adding various other constraints of the aircraft;
a trajectory planning problem model processing module 903, configured to process the trajectory planning problem model to obtain a processed trajectory planning problem model;
an initial reference trajectory generation module 904 for generating an available initial reference trajectory according to desired initial and terminal conditions;
and a collaborative reentry trajectory solving module 905, configured to determine a collaborative reentry trajectory of multiple aircraft by using a sequence convex optimization method according to the processed trajectory planning problem model and the initial reference trajectory.
The multi-aircraft cooperative reentry trajectory planning system provided by the embodiment of the invention is similar to the multi-aircraft cooperative reentry trajectory planning method described in the embodiment in working principle and beneficial effect, so detailed description is omitted here, and specific content can be referred to the introduction of the embodiment of the method.
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 are communicated with each other through the bus. The processor may invoke a computer program in memory to perform the multi-aircraft collaborative reentry trajectory planning method.
Further, the computer program stored in the memory described above may be stored in a computer-readable storage medium when it is implemented in the form of a software functional unit and sold or used as a separate product. Based on such understanding, the technical solution of the present invention or a part thereof which substantially contributes to the prior art may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: u disk, removable hard disk, read only memory, random access memory, magnetic or optical disk, etc. for storing program codes.
Further, the present invention also provides a non-transitory computer readable storage medium, on which a computer program is stored, and when the computer program is executed, the method for planning a multi-aircraft collaborative reentry trajectory may be implemented.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. A multi-aircraft collaborative reentry trajectory planning method is characterized by comprising the following steps:
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;
establishing terminal time constraints according to the improved aircraft dynamics model, and determining a trajectory planning problem model by adding other constraints of the aircraft;
processing the track planning problem model to obtain a processed track planning problem model;
generating an available initial reference trajectory according to desired initial and terminal conditions;
and determining the multi-aircraft cooperative reentry trajectory by adopting a sequence convex optimization method according to the processed trajectory planning problem model and the initial reference trajectory.
2. The method for planning the multi-aircraft cooperative reentry trajectory according to claim 1, wherein the building of a dynamic model of the aircraft and the modifying of the dynamic model by redefining the independent variables generate a modified dynamic model of the aircraft specifically comprises:
establishing a dynamic model of the hypersonic glide aircraft; the dynamic model adopts a kinematics equation with time t as an independent variable to describe the unpowered gliding process of the reentry section of the aircraft;
by redefining normalized time tau epsilon [0,1]Modifying the dynamics model for independent variables to generate a modified aircraft dynamics model
Wherein x = [ r, theta, phi, v, gamma, psi, sigma, t] T Is a flight state vector; r is the distance from the geocenter to the aircraft, θ and φ represent longitude and latitude, respectively, v is the flight velocity of the aircraft relative to the earth, γ and ψ are the ballistic inclination angle and the velocity heading angle, respectively, and σ is the roll angle; u. of σ Is the rate of change of roll angle; amount of time control
f(x,u σ ) And f Ω (x,u σ ) Terms representing no and with earth rotation angular velocities in the improved aircraft dynamics model, respectively.
3. The multi-aircraft collaborative reentry trajectory planning method according to claim 2, wherein the establishing of the terminal time constraint according to the improved aircraft dynamics model and the determination of the trajectory planning problem model by the addition of other constraints of the aircraft specifically include:
establishing terminal time constraint according to the improved aircraft dynamics model, and determining a trajectory planning problem model by adding other constraints of the aircraft
Wherein J represents the function of optimization, wherein,
representing the heat flow density;
n max ,q max are respectively aircraft energy bearingDensity of received heat flow
Non-dimensionalized maximum values of overload n and dynamic pressure q; g 1 -g 3 Functional expression representing a constraint, K Q Is the heat flux density constant, ρ is the atmospheric density, and L and D are the lift and drag accelerations, respectively; sigma max Is the limiting value of the roll angle; u. of σmax Is the clipping value of the roll angle rate of change;
is the desired total time of flight; r is 0 ,θ 0 ,φ 0 ,v 0 ,γ 0 ,ψ 0 Respectively representing initial state quantities; r is a radical of hydrogen f ,θ f ,φ f ,v f ,γ f ,ψ f Respectively representing the terminal time state quantities; v. of fmin ，v fmax Respectively representing the minimum and maximum values of the desired terminal speed.
4. The multi-aircraft collaborative reentry trajectory planning method according to claim 3, wherein the processing the trajectory planning problem model to obtain a processed trajectory planning problem model specifically comprises:
carrying out linearization processing and convexity processing on the track planning problem model based on a small disturbance linearization method, and converting the track planning problem model P0 into a continuous convex optimization problem model P1;
and carrying out discretization processing on the continuous convex optimization problem model P1 to obtain a processed trajectory planning problem model P2.
5. The multi-aircraft cooperative re-entry trajectory planning method according to claim 4, wherein the generating of the available initial reference trajectory according to the desired initial and terminal conditions specifically comprises:
determining an initial sequence of control quantities based on desired initial and terminal conditions
Wherein
And
respectively representing the roll angle change rate control amount and the time control amount of the i discrete points;
and substituting the control quantity initial sequence into the track planning problem model P0, and generating an available initial reference track through fourth-order Runge-Kuta numerical integration.
6. A multi-aircraft collaborative reentry trajectory planning system, comprising:
the aircraft modeling and model improving module is used for establishing a dynamic model of the aircraft, improving the dynamic model by redefining independent variables and generating an improved dynamic model of the aircraft;
the trajectory planning problem model establishing module is used for establishing terminal time constraint according to the improved aircraft dynamics model and determining a trajectory planning problem model by adding other constraints of the aircraft;
the track planning problem model processing module is used for processing the track planning problem model to obtain a processed track planning problem model;
an initial reference track generation module for generating an available initial reference track according to desired initial and terminal conditions;
and the cooperative reentry trajectory solving module is used for determining the cooperative reentry trajectory of the multiple aircrafts by adopting a sequence convex optimization method according to the processed trajectory planning problem model and the initial reference trajectory.
7. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor, when executing the computer program, implements the multi-aircraft collaborative reentry trajectory planning method of any of claims 1 to 5.
8. A non-transitory computer readable storage medium having stored thereon a computer program, wherein the computer program when executed implements the multi-aircraft collaborative reentry trajectory planning method of any of claims 1 to 5.
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