CN115950310A - Attack time and angle constraint guidance method of time-varying speed aircraft - Google Patents
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Abstract
The invention discloses an attack time and angle constraint guidance method of a time-varying speed aircraft, which comprises the following steps: establishing a mathematical model of the missile and the target by taking a two-dimensional horizontal plane where the missile and the target are positioned as an attack plane; generating a two-stage flight track meeting flight time, a terminal angle and maximum overload constraint by adopting a second-order Bezier curve based on a mathematical model of a missile and a target; converting the generated two-stage flight trajectory into a time sequence path point; and tracking the obtained time sequence path point by utilizing a PLOS (programmable logic operation) track tracking algorithm to generate a guidance instruction. The guidance method provided by the invention not only can meet the attack time and angle constraints of the missile target at a constant speed, but also has excellent control effects on the attack time and the attack angle at an unsteady speed.
Description
Technical Field
The invention belongs to the field of guidance and control of an aerospace vehicle, and relates to an attack time and angle constraint guidance method of a time-varying speed aircraft.
Background
The design focus of the traditional guidance law is the miss distance between an aircraft and a target, but under some special situations, constraints such as attack time, attack angle and the like also need to be considered, for example, in order to improve the missile penetration effect or the damage efficiency of a warhead, the missile needs to approach the target at a specific angle, and the control of the attack angle becomes particularly important at this moment; when multiple flying missiles need to carry out saturated cooperative attack to break through the short-range defense system of the naval vessel, the control of attack time becomes particularly important.
Therefore, the attack time and angle constraint guidance law has wide application, can enable the aircraft to reach the designated position at the given time and angle, and has important application value for the cooperative flight of multiple aircrafts. However, the existing attack time and angle constraint guidance method is not suitable for the aircraft with variable speed, and the controllable range of the flight time cannot be given according to the initial condition.
Most of the guidance laws are designed based on a time domain control method, the flight tracks guided by the guidance laws are implicit, most of the attack time and angle constraint guidance laws are designed based on the time domain control method, the flight tracks guided by the guidance laws are implicit, accurate estimation of the residual flight time becomes a great difficulty, and the number of documents for researching the attack time and angle constraint guidance laws is small. Many scholars adopt a small course angle hypothesis to carry out linear estimation on the residual flight time when studying the attack time and the angle constraint guidance law, and the time estimation method can generate larger deviation when the terminal angle is larger, thereby greatly reducing the guidance performance; in addition, many existing two-dimensional attack time and angle constraint guidance laws cannot obtain a controllable range of flight time according to initial conditions, cooperation time is often selected from intersection of flight time ranges of all projectiles for cooperation of the projectile groups, and success of cooperation of the projectile groups is difficult to guarantee if the controllable time range is not used as a basis.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides an attack time and angle constraint guidance method for a time-varying speed aircraft.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
an attack time and angle constraint guidance method for a time-varying speed aircraft comprises the following steps:
establishing a mathematical model of the missile and the target by taking a two-dimensional horizontal plane where the missile and the target are positioned as an attack plane;
generating a two-stage flight track meeting flight time, a terminal angle and maximum overload constraint by adopting a second-order Bezier curve based on a mathematical model of a missile and a target;
converting the generated two-stage flight trajectory into a time sequence path point;
and tracking the obtained time sequence path point by utilizing a PLOS (programmable logic operation) track tracking algorithm to generate a guidance instruction.
Further, the mathematical model of the missile is as follows:
the speed of the missile varies as a function of the thrust and aerodynamic resistance of the missile:
wherein V represents the velocity of the missile, P en Representing the thrust of the missile, m representing the mass of the missile, S representing the reference area, p representing the air density, C D Representing a drag coefficient;
m and P en Given according to the actual parameters of the missile, all are functions comprising time t:
wherein, T en Represents thrust force,. Mu.represents fuel consumption rate, m 0 Representing the initial total mass of the missile, m fu Representing fuel mass, t en Indicating the maximum operating time of the engine.
The flying motion of the missile on the two-dimensional attack plane is as follows:
|a|≤a max
the relative distance r and the line of sight angle LOS vary as:
wherein V represents the velocity of the missile, a represents the normal acceleration, a max Representing the upper limit of the magnitude of the acceleration, (x) m ，y m ) T The position information of the missile is represented, R represents the distance between the missile and the target, theta represents the course angle of the missile, lambda represents the line of sight (LOS), and theta represents f The expected terminal angle is represented, sigma represents the included angle between the missile course and the line of sight (LOS), and the positive direction of the angle is the anticlockwise direction.
Further, the missile initial position is set to be (0,0) T The target position is (x) t ，0) T The mathematical model of the target is:
wherein (x) m ，y m ) T Indicating the location information of the missile (x) t ，y t ) T Indicating the position information of the target point, theta indicating the course angle of the missile, t f Representing the terminal time, theta f Indicating the desired terminal angle.
Further, a straight-line track line in the two-stage flight path is defined by a target point position (x) t ，0) T And terminal angle theta f Determining that the expression is as follows:
y＝tan(θ f )(x-x t )
the second-order Bezier curve is formed by the initial position
Track switch point>
And control point Q (x) Q ，y Q ) Determining that the expression is as follows:
B(τ)＝(1-τ) 2 E 1 +2(1-τ)τQ+τ 2 E 2
wherein tau represents a curve parameter with a value in an interval [0,1 ].
Control point Q (x) Q ，y Q ) The positions of (A) are:
wherein, theta 0 Representing the initial track angle, θ f Indicating the desired terminal angle.
Further, the time-of-flight constraint is:
length L and point E of two-stage flight path 2 Is expressed by the following formula:
the analytic solution of the two-stage flight path length L is as follows:
wherein J = E 1 -2Q+E 2 、K＝Q-E 1 ，D＝(J·K)/|J| 2 ，E＝|K| 2 /|J| 2 ，u＝τ+D，U＝E-D 2 、
E＝|K| 2 /|J| 2 ，W＝J+K。
The two-section flight path length L and the flight time meet the requirement of the missile on the whole flight time period [0,t ] f ]The distance of flying at the unsteady speed V (t) is equal to the length L of the two-section flight path, and the missile flies at t f The time reaches a predetermined position, and therefore reaches a time t f And track switching point
Satisfies the following relationship β:
wherein sigma represents the included angle between the missile heading and the line-of-sight angle LOS.
Further, the terminal angle constraint is as follows:
further, the acceleration command of missile flight is closely related to the curvature of the flight path, and the maximum overload constraint is as follows:
|k(τ)| max ≤a max /V 2 ,τ∈[0,1]
wherein | k (τ) emitting max Maximum curvature of two-segment flight path, segment initial position E 1 And a target position E 2 Is M, then | k (τ) & gtis zero max Can be expressed as:
further, the two-stage flight trajectory generation process is as follows:
searching the upper limit t and the lower limit t of the feasible arrival time by using an optimization algorithm according to the missile flight time, the terminal angle and the maximum overload constraint fmin And t fmax The objective function for searching the adjustable range of the arrival time is as follows:
given a desired arrival time t f Under the condition of (1), searching a corresponding track switching point E 2 The objective function of the search process is:
calculating a two-section flight track parameter equation according to the following formula and the obtained track switching point:
further, the process of converting the two-stage flight trajectory into the time sequence path point is as follows:
let Δ L s (i) The distance of the missile in the time period from delta t (i-1) to delta t & i is calculated, then
ΔL s (i)＝|B′(τ)|·Δτ＝V(Δt·(i-1))·Δt
Wherein, V (Δ t · (i-1)) represents the missile flight speed at Δ t · (i-1), Δ t represents the simulation step length, Δ τ represents the variation of the curve parameter in Δ t time, B '(τ) represents the slope of the second-order Bezier curve, | B' (τ) | may be expressed as:
obtaining the matching relation between the curve parameter tau and the flight time t by using a numerical iteration method:
setting an initial time t =0, an initial iteration number i =0 and an initial curve parameter τ 0 ＝0；
Setting DeltaL according to the time-varying curve of flight distance s (i) And calculating a curve parameter τ corresponding to the iteration number i, time t according to the following formula:
τ i ＝τ i-1 +ΔL s (i)/|B′(τ)|；
updating time t = t + Δ t, and continuously repeating iteration until the curve parameter τ reaches its upper bound 1;
after the iteration process, the time sequence path point taking the flight time t as the reference can be obtained.
Further, the PLOS trajectory tracking algorithm is:
set up W i ＝(x i ,y i ),W i+1 ＝(x i+1 ,y i+1 ),I,θ,k 1 ,k 2 The initial value of the V parameter;
calculating theta d ＝atan 2(y i+1 -y,x i+1 -x)；
Calculating out
Solving the guidance law to theta PLOS ＝k 1 (θ d -θ)+k 2 d；
Wherein k is 1 ,k 2 As algorithm parameters, the guidance instruction comprises a pure tracking guidance law and an LOS guidance law:
pure tracking guidance law:
θ P ＝k 1 (θ d -θ)
LOS guidance law:
θ LOS ＝k 2 d
wherein I represents the position of the missile at the moment t, W i And W i+1 Representing the path points which are in front of and behind the missile and are closest to the missile at time t, theta representing the course angle of the missile d Representing a vector
Angle theta with positive direction of x-axis of coordinate system P Represents a vector pick>
An included angle with the positive direction of the x axis of the coordinate system, and d represents the missile and the vector->
The vertical distance of (a).
Compared with the prior art, the invention has the following beneficial effects:
the invention provides an attack time and angle constraint guidance method of a time-varying speed aircraft, which ensures the smooth transition of a two-stage flight track and the adjustability of the track length through a second-order Bezier curve. The terminal angle constraint is realized by flying the missile along the given collision trajectory line, and the length of the trajectory is adjusted by adjusting the trajectory switching point, so that the flying time is controlled. In order to ensure that the missile can fly along the obtained track under the limited overload capacity, the track curvature constraint is fully considered in the track design, and the constraint further limits the adjusting range of the track switching point. On the basis, a feasible flight time range is obtained by using a numerical method, and controllability of the arrival time is enhanced. And finally, tracking the designed flight track by using a PLOS algorithm, so that the missile can fly along the set track under the factors such as the time delay of an autopilot and the like. A missile motion model containing engine thrust and resistance is established, and an attack time and angle constraint trajectory planning method suitable for a time-varying speed aircraft is designed. The guidance method provided by the invention not only can meet the attack time and angle constraints of the missile target at a constant speed, but also has excellent control effects on the attack time and the attack angle at an unsteady speed.
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In order to more clearly explain the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention, and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a guidance and control flow diagram of the present invention.
FIG. 2 is a two-dimensional guidance situation diagram of the present invention.
FIG. 3 is a schematic diagram of track generation based on a second-order Bezier curve according to the present invention.
FIG. 4 is a schematic diagram of the trajectory tracking strategy of the present invention.
FIG. 5 is a graph of the time variation of the flight speed and flight distance of the missile of the invention.
FIG. 6 is a diagram showing the simulation result of single bullet guidance at a constant velocity according to the present invention.
FIG. 7 is a diagram of the result of the single shot guidance simulation at unsteady velocities in accordance with the present invention.
Wherein, fig. 5 (a) is a graph of the change of the flying speed of the missile with time, fig. 5 (b) is a graph of the change of the flying distance of the missile with time, fig. 6 (a) is a graph of the flying track of the missile at a constant speed, fig. 6 (b) is a graph of the relative distance of the missile at the constant speed with time, fig. 6 (c) is a graph of the change of the acceleration at the constant speed with time, fig. 6 (d) is a graph of the change of the heading angle at the constant speed with time, fig. 7 (a) is a graph of the flying track of the missile at an unsteady speed, fig. 7 (b) is a graph of the relative distance of the missile at an unsteady speed with time, fig. 7 (c) is a graph of the change of the acceleration at the unsteady speed with time, and fig. 7 (d) is a graph of the change of the heading angle at the unsteady speed with time.
Detailed Description
The following description of the exemplary embodiments of the present application, taken in conjunction with the accompanying drawings, includes various details of the embodiments of the application for the understanding of the same, which are to be considered exemplary only. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the present application. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.
It is to be understood that the embodiments described are only a few embodiments of the present application and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
It should be noted that the terminal in the embodiments of the present application may include, but is not limited to, a mobile phone, a Personal Digital Assistant (PDA), a wireless handheld device, a Tablet Computer (Tablet Computer), a Personal Computer (PC), an MP3 player, an MP4 player, a wearable device (e.g., smart glasses, smart watches, smart bracelets, etc.), a smart home device, and other smart devices.
In addition, the term "and/or" herein is only one kind of association relationship describing an associated object, and means that there may be three kinds of relationships, for example, a and/or B, which may mean: a exists alone, A and B exist simultaneously, and B exists alone. In addition, the character "/" herein generally indicates that the former and latter associated objects are in an "or" relationship.
The invention is described in further detail below with reference to the accompanying drawings:
referring to fig. 1, the invention provides an attack time and angle constraint guidance method for a time-varying speed aircraft, which comprises the following steps:
step 1: and establishing a mathematical model of the missile and the target by taking a two-dimensional horizontal plane where the missile and the target are positioned as an attack plane according to the guidance situation shown in figure 2.
The velocity change of the missile can be represented as P en And aerodynamic drag:
wherein V represents the velocity of the missile, P en Representing the thrust of the missile, m representing the mass of the missile, S representing the reference area, p representing the air density, C D Representing the drag coefficient.
m and P en Given according to the actual parameters of the missile, all are functions comprising time t:
wherein, T en Represents thrust force,. Mu.represents fuel consumption rate, m 0 Representing the initial total mass of the missile, m fu Representing fuel mass, t en Indicating the maximum operating time of the engine.
The flight motion of the missile in the two-dimensional plane can be represented as:
|a|≤a max
the change in relative distance r and line of sight angle LOS can be expressed as:
wherein V represents the velocity of the missile, a represents the normal acceleration, a max Represents the upper limit of the acceleration amplitude value (x) m ，y m ) T Indicating the position information of the missile, R indicating the distance between the missile and the target, theta indicating the course angle of the missile, lambda indicating the line-of-sight angle LOS, theta f The expected terminal angle is represented, sigma represents the included angle between the missile heading and the line-of-sight angle LOS, and the positive direction of the angle is the counterclockwise direction.
The goal of flight trajectory planning is to have the aircraft at a given terminal time t f When a given course angle is reached, the target position is reached, and the mathematical model of the target is as follows:
wherein (x) m ，y m ) T Indicating the position information of the missile (x) t ，y t ) T Indicating the position information of the target point, theta indicating the course angle of the missile, t f Representing the terminal time, theta f Indicating the desired terminal angle, set the missile initial position to (0,0) T The target position is (x) t ，0) T 。
And 2, step: and generating a two-stage flight track meeting the flight time, the terminal angle and the maximum overload constraint through a second-order Bezier curve. Firstly, designing a linear collision track meeting the terminal angle constraint; and designing a curve for transferring the missile from the launching point to a linear collision track along the initial velocity vector. The two curves respectively correspond to the final section and the initial section of missile flight, and the position of the missile entering the collision track is called a track switching point. The trace generation diagram is shown in fig. 3.
The straight line is defined by the target point position (x) t ，0) T And terminal angle theta f DeterminingThe expression is:
y＝tan(θ f )(x-x t ) (8)
where x represents the abscissa of the two-dimensional plane and y represents the ordinate of the two-dimensional plane.
The second-order Bezier curve is formed by an initial position
Track switching point->
And control point Q (x) Q ，y Q ) Determining that the expression is:
B(τ)＝(1-τ) 2 E 1 +2(1-τ)τQ+τ 2 E 2 (9)
wherein tau represents a curve parameter with a value in an interval [0,1 ].
Setting E 1 Is the origin of the inertial system, target position E 2 For the trajectory switching point, control point Q is at the intersection I of the launch trajectory line and the collision trajectory line, control point Q (x) Q ，y Q ) The position of (c) can be calculated as:
wherein, theta 0 Representing the initial track angle, theta f Indicating the desired terminal angle.
Length L and point E of two-stage flight path 2 Can be expressed by the following formula:
for convenient calculation, the analytic solution of the two-stage flight path length L is:
wherein J = E 1 -2Q+E 2 、K＝Q-E 1 ，D＝(J·K)/|J| 2 ，E＝|K| 2 /|J| 2 ，u＝τ+D，U＝E-D 2 、
E＝|K| 2 /|J| 2 ，W＝J+K。
The constraints of flight time on flight trajectory are:
the two-section flight path length L and the flight time meet the requirement of the missile on the whole flight time period [0,t ] f ]The distance of flight at unsteady speed V (t) is equal to the length L of two-stage flight path, and the missile at t f The time reaches a predetermined position, and therefore reaches a time t f And track switching point
The following relationship β is satisfied:
wherein sigma represents the included angle between the missile heading and the line-of-sight angle LOS.
The constraint of the terminal angle on the flight trajectory is as follows:
the maximum overload constrains the flight trajectory to:
the acceleration command of missile flight is closely related to the curvature of the flight trajectory, so that the maximum curvature of the trajectory satisfies the following conditions:
|k(τ)| max ≤a max /V 2 ,τ∈[0,1] (15)
wherein | k (τ) emitting max Maximum curvature of two-segment flight path, segment initial position E 1 And a target position E 2 Is M, then | k (τ) ceiling max Can be expressed as:
searching the upper limit t and the lower limit t of the feasible arrival time by using an optimization algorithm according to the missile flight time, the terminal angle and the maximum overload constraint fmin And t fmax The objective function for searching the adjustable range of the arrival time is as follows:
the two-stage flight path generation process comprises the following steps:
given t f Under the condition of (expected arrival time), searching a corresponding track switching point E 2 The objective function of the search process is:
wherein | k (τ) emitting max Defining a line segment E for maximum curvature of the two-segment trajectory 1 E 2 Is M, then | k (τ) ceiling max Can be expressed as:
calculating a flight track parameter equation according to the equation (20) and the obtained track switching point:
and step 3: and converting the design track into a time sequence path point.
From a differential point of view, the curve can be regarded as a straight line in a sufficiently small part, let Δ L s (i) The distance of the missile in the time period from delta t (i-1) to delta t & i is calculated, then
ΔL s (i)＝|B′(τ)|·Δτ＝V(Δt·(i-1))·Δt (21)
Wherein V (Δ t · (i-1)) represents the missile flight speed at Δ t · (i-1), Δ t represents the simulation step size, Δ τ represents the variation of the curve parameter in Δ t time, B '(τ) represents the slope of a second-order Bezier curve, | B' (τ) | may be expressed as:
the matching relation between the curve parameter tau and the flight time t is obtained by using a numerical iteration method as follows:
1. firstly, initialization setting is carried out, wherein an initial time t =0, an initial iteration number i =0 and an initial curve parameter tau are set 0 ＝0；
2. Setting DeltaL according to the time-varying curve of the flight distance s (i) And calculating a curve parameter tau corresponding to the iteration number i and the time t according to the following formula i ＝τ i-1 +ΔL s (i)/|B′(τ)|；
3. Updating the time t = t + Δ t, and continuously repeating the steps 2 and 3 until the curve parameter τ reaches the upper bound 1;
after the iteration process, the path point with the flight time t as the reference can be obtained.
And 4, step 4: and tracking the path points obtained in the step 3 by using a PLOS trajectory tracking algorithm, and keeping the trajectory tracking error at a small level, wherein the trajectory tracking error d is defined as shown in FIG. 4.
The trajectory tracking algorithm is as follows:
1. initialization, setting W i ＝(x i ,y i ),W i+1 ＝(x i+1 ,y i+1 ),I,θ,k 1 ,k 2 The initial value of the V parameter;
2. calculating theta d ＝atan 2(y i+1 -y,x i+1 -x)；
3. Computing
4. Solving the guidance law to theta PLOS ＝k 1 (θ d -θ)+k 2 d。
Wherein k is 1 ,k 2 As an algorithm parameter, the guidance instruction contained by the PLOS consists of two parts:
pure tracking guidance law:
θ P ＝k 1 (θ d -θ) (23)
LOS guidance law:
θ LOS ＝k 2 d (24)
wherein I is the position of the missile at time t, W i And W i+1 Is a path point which is positioned in front of and behind the missile and is closest to the missile at time t, theta is the course angle of the missile, and theta is the angle of the missile u Is a vector
Angle theta with positive direction of x-axis of coordinate system d Is a vector
Angle theta to the positive direction of the x-axis of the coordinate system p Is a vector>
An included angle with the positive direction of the x axis of the coordinate system, and d is the missile and the vector>
The vertical distance of (a).
Example 1:
the effectiveness and the superiority of the trajectory planning method provided by the invention are verified by taking the trajectory planning of a single missile at a constant speed and an unsteady speed as an example.
The missile using the guidance method of the invention is called missile 1 for short, and the missile using the other existing guidance method is called missile 2 for short. The simulation parameters are set as follows:
(1) The missile engine is a single-chamber single-thrust solid engine with thrust T en 10000N, the maximum working time t of the engine en Is 10s, burnInitial total weight m of material fu 100kg, a specific fuel consumption of 10kg/s, a maximum missile overload a max Is 200m/s 2 The position of the target is (10000,0) T m。
(2) The simulation time step is set to be 0.001s, and the time constant of the missile flight control system is considered. Because the time interval exists between the receiving of the instructions and the execution of the instructions in the flight control system of the missile, the actual flight track of the missile deviates from the established track, and the robustness of a guidance algorithm can be tested by adding the time constant of the flight control system in the simulation. In the simulation, the flight control system is equivalent to a first-order inertia link with a time constant of 0.2 s.
(3) Parameter k in PLOS trajectory tracking algorithm 1 ,k 2 Set to 60 and 3, respectively.
The distance and speed curves of the missile obtained through simulation according to the parameter settings are shown in fig. 5.
1. Trajectory planning for single missile at constant speed
Setting the flying speed of the missile to be 300m/s and the launching angle to be theta 0 =60 °, desired end angle θ f = 65 °, missile launch time 0s. Adopting a gradient-free optimization algorithm, namely an Adaptive grid Direct Search algorithm (MADS):
1. according to the target function formula (19) and the terminal angle theta f Calculating upper and lower limits t of search available arrival time by using MADS algorithm fmin ＝48.27s、t fmax ＝63.21s。
2. From the resulting feasible arrival time ranges [48.27, 63.21]s, selecting the expected arrival time as t f ＝50s。
3. And (3) generating a flight track parameter equation meeting the time and angle constraints by using the track generation algorithm in the step (2).
4. Converting the obtained track parameter equation into a time-based path point according to the step 3;
5. and calculating a guidance instruction according to the step 4.
The simulation result is shown in FIG. 6, in which FIG. 6 (a) shows the flight paths of missile 1 and missile 2The trace in the figure shows that two missiles successfully reach the given target; as can be seen from the variation curve of the relative distance between the eyes shown in fig. 6 (b), the actual arrival time of the missile 2 is t =50.51s, which is slightly later than the expected time, and this result confirms the estimated remaining flight time t of the missile 2 go The linear estimation method adopted in the time is not accurate enough, the estimation error is increased by a larger terminal angle, and compared with the missile 1, the missile accurately reaches the target at t =50s, because the guidance method realizes the flight time cooperative convergence by coordinating the track length, the time cooperative performance is excellent; fig. 6 (c) shows acceleration curves of two missiles during flight, wherein the step of missile 1 at t =45.31s corresponds to the trajectory switching process of the guidance law provided in this chapter; FIG. 6 (d) shows the variation of the flight heading angle, indicating that both missiles 1 and 2 achieve the desired terminal angle at the terminal time.
The two guidance methods are compared below from the point of view of energy consumption, the energy consumption cost function being defined as the integral of the square of the acceleration command, i.e.
The energy consumption of the guidance method is 7268.3J and the energy consumption of the other guidance method is 11050.1J. It is clear that the control energy required for the guidance method in the present invention is reduced by 34.22%. Meanwhile, the trajectory shape in fig. 6 (a) and the missile eye distance curve in fig. 6 (b) show that in order to satisfy the constraints of arrival time and terminal angle, missile 2 has an "S" shaped trajectory in the flight process, which results in an increase in control energy and a decrease in missile terminal speed in practical use, compared with missile 1 that realizes time and angle control by a smooth second-order Bezier curve to reduce energy consumption, the difference in energy consumption of the two guidance methods mainly results from that missile 1 has a complete plan for the flight process before launching, and missile 2 does not have.
2. Trajectory planning for single missile at unsteady speed
The velocity of the missile is set to an unsteady velocity as shown in fig. 5, but other simulation conditions are the same as those in the case of the above-described steady velocity.
1. According to the target function formula (19) and the terminal angle theta f Calculating upper and lower limits t of search available arrival time by MADS algorithm fmin ＝26.54s、t fmax ＝31.17s。
2. From the resulting range of feasible arrival times [26.54, 31.17]s, selecting the expected arrival time as t f ＝30s。
3. And (3) generating a flight trajectory parameter equation meeting the time and angle constraints by using the trajectory generation algorithm in the step (2).
4. Converting the obtained track parameter equation into a time-based path point according to the step 3;
5. and calculating a guidance instruction according to the step 4.
The simulation results are shown in fig. 7. The flight trajectory in fig. 7 (a) and the projectile distance curve in fig. 7 (b) show that both missile 1 and missile 2 successfully reach a given target at the desired angle, with arrival times of 30.06s and 36.43s, respectively. The unsteady speed hardly influences the performance of the proposed guidance method, because the flight distance of the unsteady speed missile in given time is known, the trajectory planning method can accurately control the trajectory length to match with the missile flight time, and excellent time cooperative convergence is realized. FIG. 7 (c) is an acceleration curve of two missiles in the flight process, and comparison of the two curves shows that the acceleration instruction of the guidance method is more stable, and the guidance instruction generated by the missile 2 guidance law oscillates. FIG. 7 (d) is a course angle variation curve during flight, which shows that both missiles achieve the predetermined terminal angle constraint.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. An attack time and angle constraint guidance method of a time-varying speed aircraft is characterized by comprising the following steps:
establishing a mathematical model of the missile and the target by taking a two-dimensional horizontal plane where the missile and the target are positioned as an attack plane;
generating a two-stage flight track meeting flight time, a terminal angle and maximum overload constraint by adopting a second-order Bezier curve based on a mathematical model of a missile and a target;
converting the generated two-stage flight trajectory into a time sequence path point;
and tracking the obtained time sequence path point by utilizing a PLOS (programmable logic operation) track tracking algorithm to generate a guidance instruction.
2. The attack time and angle constraint guidance method of the time-varying speed aircraft according to claim 1, characterized in that the mathematical model of the missile is as follows:
the speed of the missile varies as a function of the thrust and aerodynamic resistance of the missile:
wherein V represents the velocity of the missile, P en Representing the thrust of the missile, m representing the mass of the missile, S representing the reference area, p representing the air density, C D Representing a drag coefficient;
m and P en Given according to the actual parameters of the missile, all are functions comprising time t:
wherein, T en Represents thrust force,. Mu.represents fuel consumption rate, m 0 Represents the initial total mass of the missile, m fu Representing fuel mass, t en Representing a maximum operating time of the engine;
the flying motion of the missile on the two-dimensional attack plane is as follows:
|a|≤a max
the variation of the relative distance r and the line of sight angle LOS is:
wherein V represents the velocity of the missile, a represents the normal acceleration, a max Represents the upper limit of the acceleration amplitude value (x) m ，y m ) T Indicating the position information of the missile, R indicating the distance between the missile and the target, theta indicating the course angle of the missile, lambda indicating the line-of-sight angle LOS, theta f The expected terminal angle is represented, sigma represents the included angle between the missile heading and the line-of-sight angle LOS, and the positive direction of the angle is the counterclockwise direction.
3. The time-varying speed aircraft attack time and angle constraint guidance method as claimed in claim 1, characterized in that the missile initial position is set as (0,0) T The target position is (x) t ，0) T The mathematical model of the target is:
wherein (x) m ，y m ) T Indicating the position information of the missile (x) t ，y t ) T Indicating the position information of the target point, theta indicating the course angle of the missile, t f Representing the terminal time, theta f Indicating the desired terminal angle.
4. The time-varying speed aircraft attack time and angle constraint guidance method according to claim 1, characterized in that a straight-line trajectory in the two-stage flight trajectory is defined by a target point position (x) t ，0) T And terminal angle theta f Determining that the expression is as follows:
y＝tan(θ f )(x-x t )
the second-order Bezier curve is formed by an initial position
Track switch point>
And control point Q (x) Q ，y Q ) Determining that the expression is as follows:
B(τ)＝(1-τ) 2 E 1 +2(1-τ)τQ+v 2 E 2
wherein tau represents a curve parameter with a value in an interval [0,1 ];
control point Q (x) Q ，y Q ) The positions of (A) are:
wherein, theta 0 Representing the initial track angle, theta f Indicating the desired terminal angle.
5. The time-varying speed aircraft attack time and angle constraint guidance method according to claim 1, characterized in that the time-of-flight constraint is:
length L and point E of two-stage flight path 2 Is expressed by the following formula:
the analytic solution of the two-stage flight path length L is as follows:
wherein J = E 1 -2Q+E 2 、K＝Q-E 1 ，D＝(J·K)/|J| 2 ，E＝|K| 2 /|J| 2 ，u＝τ+D，U＝E-D 2 、
E＝|K| 2 /|J| 2 ，W＝J+K；
The two-section flight path length L and the flight time satisfy the whole flight time period of the missile 0,t f ]The distance of flying at the unsteady speed V (t) is equal to the length L of the two-section flight path, and the missile flies at t f The time reaches a predetermined position, and therefore reaches a time t f And track switching point
Satisfies the following relationship β:
wherein sigma represents the included angle between the missile course and the line of sight angle LOS.
6. The attack time and angle constraint guidance method for the time-varying speed aircraft according to claim 1, characterized in that the terminal angle constraint is as follows:
7. the time-varying speed aircraft attack time and angle constraint guidance method according to claim 1 is characterized in that the acceleration command of missile flight is closely related to the curvature of flight trajectory, and the maximum overload constraint is as follows:
|k(τ)| max ≤a max /V 2 ，τ∈[0，1]
wherein | k (τ) emitting max Maximum curvature of two-segment flight path, segment initial position E 1 And target position E 2 Is M, then | k (τ) ceiling max Can be expressed as:
8. the attack time and angle constraint guidance method of the time-varying speed aircraft as claimed in claim 1, characterized in that the two-stage flight trajectory generation process is:
searching by using an optimization algorithm according to the flying time of the missile, the terminal angle and the maximum overload constraintUpper and lower limits t of feasible arrival time fmin And t fmax The objective function for searching the adjustable range of the arrival time is as follows:
min or max t f
|k(τ)| max ≤a max /V 2 ，τ∈[0，1]
given a desired arrival time t f Under the condition of (2), searching a corresponding track switching point E 2 The objective function of the search process is:
|k(τ)| max ≤a max /V 2 ，τ∈[0，1]
calculating a two-section flight track parameter equation according to the following formula and the obtained track switching point:
9. the attack time and angle constraint guidance method for the time-varying speed aircraft according to claim 1, characterized in that the process of converting the two-stage flight path into the time sequence path point is as follows:
let Δ L s (i) The distance of the missile in the time period from delta t (i-1) to delta t & i is calculated, then
ΔL s (i)＝|B′(τ)|·Δτ＝V(Δt·(i-1))·Δt
Wherein V (Δ t · (i-1)) represents the missile flight speed at Δ t · (i-1), Δ t represents the simulation step length, Δ τ represents the variation of the curve parameter in Δ t time, B '(τ) represents the slope of the second-order Bezier curve, | B' (τ) | may be expressed as:
obtaining the matching relation between the curve parameter tau and the flight time t by using a numerical iteration method:
setting an initial time t =0, an initial iteration number i =0 and an initial curve parameter τ 0 ＝0；
Setting DeltaL according to the time-varying curve of flight distance s (i) And calculating a curve parameter τ corresponding to the iteration number i, time t according to the following formula:
τ i ＝τ i-1 +ΔL s (i)/|B′(τ)|；
updating time t = t + Δ t, and continuously repeating iteration until the curve parameter τ reaches its upper bound 1;
after the iteration process, the time sequence path point taking the flight time t as the reference can be obtained.
10. The attack time and angle constraint guidance method for the time-varying speed aircraft as claimed in claim 1, wherein the PLOS trajectory tracking algorithm is as follows:
set up W i ＝(x i ，y i )，W i+1 ＝(x i+1 ，y i+1 )，I，θ，k 1 ，k 2 Initial value of the V parameter;
calculating theta d ＝atan 2(y i+1 -y，x i+1 -x)；
Computing
Solving the guidance law to theta PLOS ＝k 1 (θ d -θ)+k 2 d；
Wherein k is 1 ，k 2 The guidance instruction comprises a pure tracking guidance law and an LOS guidance law as algorithm parameters:
pure tracking guidance law:
θ P ＝k 1 (θ d -θ)
LOS guidance law:
θ LoS ＝k 2 d
wherein I represents the position of the missile at time t, W i And W i+1 Representing the path points which are in front of and behind the missile and are closest to the missile at time t, theta representing the course angle of the missile d Representing a vector
Angle theta to the positive direction of the x-axis of the coordinate system P Represents a vector pick>
An included angle with the positive direction of the x axis of the coordinate system, and d represents the missile and the vector->
The vertical distance of (c). />
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