CN112306075A - High-precision off-orbit reverse iterative guidance method - Google Patents

High-precision off-orbit reverse iterative guidance method Download PDF

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CN112306075A
CN112306075A CN202011126055.9A CN202011126055A CN112306075A CN 112306075 A CN112306075 A CN 112306075A CN 202011126055 A CN202011126055 A CN 202011126055A CN 112306075 A CN112306075 A CN 112306075A
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CN112306075B (en
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杨勇
张春阳
满益明
朱如意
王征
刘刚
邵干
张建英
刘菲
尤志鹏
曹晓瑞
黄喜元
黄世勇
王骞
沈重
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China Academy of Launch Vehicle Technology CALT
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/10—Simultaneous control of position or course in three dimensions
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Abstract

The invention discloses a high-precision off-orbit reverse iterative guidance method which comprises the following steps of: (1) according to the current position vector rnowAnd a nominal reentry velocity vector veCalculating to obtain a flight range angle to be flown, a nominal speed and a nominal reentry speed direction vector; (2) calculating to obtain the integral geocentric distance r of the current positionint‑0And vintAn integrated velocity vector for the current position; (3) iteratively integrating the endpoint velocity vector; (4) calculating to obtain a gain velocity vector vgain＝vR‑vnow(ii) a (5) Let εvIs the velocity threshold, if | vgain|>εvThen the thrust direction is output outwards
Figure DDA0002733642920000011
If | vgain|≤εvAnd if so, the engine is shut down, and the off-track guidance is finished.

Description

High-precision off-orbit reverse iterative guidance method
Technical Field
The invention relates to a high-precision off-orbit reverse iterative guidance method, and belongs to the technical field of off-orbit guidance of reusable aircrafts.
Background
The aerospace craft is a novel craft, shuttles across the atmosphere and comes and goes between the sky and the ground, and the aerospace craft has double characteristics of aerospace and aviation craft. With the rapid development of space technology and the continuous expansion of space application, a large number of aerospace aircrafts facing various task requirements are developed in succession by the aerospace major countries, a large number of new concept plans are proposed, the system composition is gradually complex, the task interfaces are easily diversified, the performance level is continuously improved, and the autonomy requirement is higher and higher.
Regarding an online guidance method, the Apollo spacecraft meets the task requirements of ground-moon transfer orbit maneuvering, rendezvous and docking and the like by using a cross-multiplication guidance law. Part of prediction projects convert off-orbit into fuel optimal control problem by constructing Hamilton function, and introduce the concept of average angular velocity to carry out gravitational acceleration linearization, obtain orbit prediction semi-analytic solution of the near-circular orbit, solve the problem of limited thrust orbital transfer of Kepler orbit, but can not meet the requirement of non-Kepler orbit reentry precision. The method is characterized in that a Unified powered flight guidance law (UPFG) in a vacuum section of the space plane is renamed to be Powered Explicit Guidance (PEG), and the bias quantity of the conditional parameters of the reentry point is iterated by combining a linear tangent guidance Law (LTG) and a high-precision orbit extrapolation method, so that the influence of the perturbation of the earth J2 gravity on the reentry point is eliminated, and the precision requirements of reentry speed, reentry angle, reentry range and the like are met.
In a single off-orbit task, for a certain fixed nominal mass, thrust and specific impulse working condition, the off-orbit point position is generally planned to be a fixed value, and whether the off-orbit point position is planned on the ground or is planned autonomously, the parameters have the condition that the measurement deviation is overlarge or unmeasurable, so that the propellant consumption and the reentry precision are influenced.
For most reentry aircrafts, the reentry point position and the reentry angle are sensitive, the reentry point speed is not sensitive, and meanwhile, the total mass, the engine thrust and the engine specific impulse of the aircraft before the departure of the aircraft are large in measurement deviation, so that the numerical values of the aircraft cannot be accurately obtained. Tgo (shutdown time) of a PEG (polyethylene glycol) off-orbit guidance law of the space shuttle calculates the current measured value of the accelerometer and the engine specific impulse value, and when the specific impulse deviation is larger, the tgo prediction deviation is correspondingly increased. Moreover, under the condition that the initial guess value is accurate, the PEG off-orbit guidance law performs high-precision orbit extrapolation at least 3 times in one guidance period, and the calculation amount is large. Due to the specific task of single brake off-rail, the re-entry speed variation range is small under conditions of limited fuel split. If the requirement of the reentry point speed is cancelled, only the position and the reentry angle of the reentry point are restricted, and the guidance process can be greatly simplified.
The deviation of the re-entry angle of the actual off-track task is required to be less than 1 degree, and the deviation of the re-entry angle of the guidance part is required to be as small as possible in consideration of respective deviations (IMU initial alignment residual deviation, thrust deviation, specific impulse deviation, control period delay and the like) of navigation and control. However, the effect of only one term of J2 perturbation on the off-track re-entry angle of the near-earth track is about 0.1 deg., so that various kinds of deviation effects need to be fully considered and eliminated. Most iterative guidance methods have the condition that the required thrust direction is changed rapidly near the shutdown point, and are not beneficial to attitude tracking. At present, the problem is mainly solved by adopting a method of keeping fixed attitude flight for a plurality of seconds before shutdown, but the problem can affect the guidance precision and needs to be solved.
Disclosure of Invention
The technical problem solved by the invention is as follows: aiming at the high-precision off-orbit requirement of the aerospace vehicle, the online off-orbit guidance method based on reverse iteration has the advantages of high precision, good deviation adaptability, good thrust direction motion linearity and small calculated amount.
The technical scheme of the invention is as follows: a high-precision off-orbit reverse iterative guidance method comprises the following steps:
(1) according to the current position vector rnowAnd a nominal reentry velocity vector veCalculating to obtain a flight range angle to be flown, a nominal speed and a nominal reentry speed direction vector;
(2) at a reentry velocity of magnitude | vBack-IterationI is an iteration initial value, and is reversely integrated from a re-entry point to a to-be-flown flight range angle delta fnowObtaining the integral earth-center distance r of the current positionint-0And vintAn integrated velocity vector for the current position;
(3) iteratively integrating the endpoint velocity vector;
(4) according to the current velocity vector vnowAnd the integrated end point velocity vector v obtained in step (3)RObtaining a gain velocity vector vgain＝vR-vnow；
(5) Let εvIs the velocity threshold, if | vgain|>εvThen the thrust direction is output outwards
Figure BDA0002733642900000031
If | vgain|≤εvAnd if so, the engine is shut down, and the off-track guidance is finished.
The specific method of the step (1) is: according to the current position vector rnowRe-entering point position vector reAnd calculating to obtain the flight range angle to be flown
Figure BDA0002733642900000032
According to the nominal reentry velocity vector veObtaining a nominal velocity ve＝|ve| and nominal reentry velocity direction vector
Figure BDA0002733642900000033
The specific method of the step (2) is as follows:
(2.1) reentry velocity magnitude | v at first calculationBack-IterationSelecting nominal speed ve(ii) a Then time-counting reentry velocity magnitude | vBack-IterationI is determined by the step (3);
(2.2) integrating the step number k and determining the reentry point position vector reIs assigned to rkThe reentry point velocity vector | vBack-Iteration|·ventry_unitAssign to vkI.e. rk＝re,vk＝|vBack-Iteration|·ventry_unit(ii) a Calculating the re-entry point to the inverse integral tkVoyage angle of time
Figure BDA0002733642900000034
Then calculate to obtain tkRemaining flight range angle delta f of timeerr,k＝Δfnow-Δft,k；
(2.3) integrating the position vector and the velocity vector by one step (k +1) to obtain an integral value r of the position vector and the velocity vectork+1,vk+1Calculating the re-entry point to the inverse integral tk+1Voyage angle of time
Figure BDA0002733642900000035
And then calculate tk+1Time residual flight distance angle delta ferr,k+1＝Δfnow-Δft,k+1；
(2.4) if Δ ferr,k·Δferr,k+1R is reassigned if the value is greater than or equal to 0k＝rk+1，vk＝vk+1，Δferr,k＝Δferr,k+1(ii) a And returning to the step (2.3) for re-execution; if Δ ferr,k·Δferr,k+1If the value is less than 0, entering the step (2.5);
(2.5) inverse integration time t as tIterationInitial value of (d), for tIterationDisturbance is carried out by delta t, and t is reassignedIteration＝tIteration+Δt；
(2.6) integrating the position vector r delta in delta t direction by one step by using an integrator to obtain a position vector r deltatAnd velocity vector vΔtCalculating to obtain the re-entry point to the inverse integral tIterationVoyage angle of time
Figure BDA0002733642900000041
Further calculating to obtain a residual flight range angle delta f to be flown at the moment of disturbance delta terr,Δt＝Δfnow-Δft,Δt；
(2.7) reassigning the at,
Figure BDA0002733642900000042
will tIterationReassign value, tIteration＝tIteration+Δt；
(2.8) integrating the position vector r in the delta t direction by one step by using an integrator to obtain a position vector rk+1,ΔtAnd velocity vector vk+1,ΔtCalculating to obtain the re-entry point to the inverse integral tIterationVoyage angle of time
Figure BDA0002733642900000043
Further calculating to obtain the residual flight range angle delta f at the time of the disturbance delta terr,k+1,Δt＝Δfnow-Δft,k+1,Δt；
(2.9) setting εfIs a range angle threshold, rint-0Is the integral geocentric distance, v, of the current positionintAn integrated velocity vector for the current position; if Δ ferr,k+1,Δt|≤εfThen carry out the assignment rint-0＝|rk+1,Δt|，vint＝vk+1,ΔtAnd entering the step (3); if Δ ferr,k+1,Δt|>εfThen carry out the assignment rk＝rk+1,Δt，vk＝vk+1,ΔtAnd returning to the step (2.5).
In the step (2.3), the integration value r of the position vector and the velocity vector is obtained by integrating one step (k +1) forward by using a variable step length Runge-Kutta method DP5(4) embedded in a Donman-Prince pairk+1,vk+1。
In the step (2.6), a 4-order Runge-Kutta integrator is used for integrating one step in the delta t direction.
The method of the step (3) comprises the following steps: comparing the distance between the earth and the heart | rnowI and rint-0If the difference between the two is larger, the speed of the re-entering point is continuously adjusted until the difference between the two is within the allowable range, and an integrated end point speed vector v is outputR＝vint-0。
The specific implementation process of the step (3) is as follows:
(3.1) setting εrIs the geocentric distance threshold, if | | | rnow|-rint-0|≤εrThen, an integrated end point velocity vector v is outputR＝vint-0Entering the step (4); if rnow|-rint-0|>εrThen, for | vBack-IterationI, disturbance is carried out on the value of delta v, and the value of | v is reassignedBack-Iteration|＝|vBack-IterationL + delta v, and executing the step (2) once to obtain the integral earth-center distance r of the current positionint-0'; for the current integral ground center distance rint-ΔvAssignment, rint-Δv＝rint-0'；
(3.2) mixing | vBack-IterationThe re-assignment of the value is,
Figure BDA0002733642900000051
and returning to the step (2).
Compared with the prior art, the invention has the beneficial effects that:
(1) in the prior art, a two-body dynamics analysis guidance means without considering the earth gravity perturbation term is generally adopted, and the deviation generated by the gravity perturbation term is calculated off line.
(2) The problem that the required thrust direction is changed rapidly near a shutdown point is solved by adopting a method for keeping a fixed attitude for a plurality of seconds before shutdown in the prior art, the motion linearity of the thrust direction output by the method is good, and the problem that the required thrust direction is changed rapidly near the shutdown point is eliminated from the source, so that the guidance precision is improved, and the control system is convenient to track.
(3) The existing iterative guidance technology generally adopts full-variable iterative search, and the calculated amount is large, but the method adopted by the invention utilizes the approximate decoupling relation of different variables and respective monotonous characteristics, and uses a layered iteration strategy, thereby effectively reducing the calculated amount and being beneficial to engineering implementation.
Drawings
Fig. 1 is a schematic diagram of inverse integration iteration.
FIG. 2 shows the flight range angle Δ fnowAnd (4) integrating a zero-crossing detection flow chart.
FIG. 3 is a flow chart of the inverse integral iterative guidance function.
Detailed Description
The invention will be described in further detail below with reference to the accompanying drawings:
a high-precision off-orbit reverse iterative guidance method is based on off-orbit segment flight angle constraint, the basic flow is as shown in figure 3, and the specific steps are as follows:
(1) according to the current position vector rnowObtaining the current geocentric distance | rnowL. According to the current position vector rnowRe-entering point position vector reCalculating the flight range angle to be flown
Figure BDA0002733642900000061
According to the nominal reentry velocity vector veObtaining a nominal velocity ve＝|ve| and nominal reentry velocity direction vector
Figure BDA0002733642900000062
According to the current position vector rnowWith the nominal reentry velocity vector veTo obtain a reentrant angle
Figure BDA0002733642900000063
The above process is as in figure 1.
(2) Magnitude of reentrant velocity | vBack-IterationI is iteration initial value from the back integral of the re-entry point to the angle delta f of the flight range to be flownnowObtaining the point integral geocentric distance rint-0As in fig. 2. The specific implementation process is as follows:
(2.1) reentry velocity magnitude | v at first calculationBack-IterationL is chosen as the nominal velocity ve. Then time-counting reentry velocity magnitude | vBack-IterationL is determined by step (3).
(2.2) integrating the step number k and determining the reentry point position vector reIs assigned to rkThe reentry point velocity vector | vBack-Iteration|·ventry_unitAssign to vkI.e. rk＝re,vk＝|vBack-Iteration|·ventry_unit. Calculating the re-entry point to the inverse integral tkVoyage angle of time
Figure BDA0002733642900000064
Calculating tkRemaining flight range angle delta f of timeerr,k＝Δfnow-Δft,k。
(2.3) integrating forward by one step (k +1) by using a variable step length Runge-Kutta method DP5(4) embedded in the Donmann-Prince pair to obtain the integral value r of the position vector and the speed vectork+1,vk+1Calculating the re-entry point to the inverse integral tk+1Voyage angle of time
Figure BDA0002733642900000065
Calculating tk+1Time residual flight distance angle delta ferr,k+1＝Δfnow-Δft,k+1。
(2.4) determination of Δ ferr,k·Δferr,k+1The symbol of (2). If Δ ferr,k·Δferr,k+1R is reassigned if the value is greater than or equal to 0k＝rk+1，vk＝vk+1，Δferr,k＝Δferr,k+1. And returning to (2.3) for re-execution. If Δ ferr,k·Δferr,k+1If less than 0, go to step (2.5).
(2.5) inverse integration time t as tIterationIs disturbed by delta t and is reassigned to tIteration＝tIteration+Δt。
(2.6) integrating the position vector r in the delta t direction by using a 4-order Runge-Kutta integrator in one stepΔtVelocity vector vΔtCalculating the re-entry point to the inverse integral tIterationVoyage angle of time
Figure BDA0002733642900000071
Calculating the residual flight range angle delta f to be flown at the moment of disturbance delta terr,Δt＝Δfnow-Δft,Δt。
(2.7) reassigning the at,
Figure BDA0002733642900000072
will tIterationReassign value, tIteration＝tIteration+Δt。
(2.8) integrating one step in the delta t direction by using a 4-order Runge-Kutta integrator to obtain a position vector rk+1,ΔtVelocity vector vk+1,ΔtCalculating the re-entry point to the inverse integral tIterationVoyage angle of time
Figure BDA0002733642900000073
Calculating the residual flight range angle delta f to be flown at the time of the disturbance delta terr,k+1,Δt＝Δfnow-Δft,k+1,Δt。
(2.9) setting εfIs a range angle threshold, rint-0Is the integral geocentric distance, v, of the current positionintIs the integrated velocity vector for the current position. If Δ ferr,k+1,Δt|≤εfThen carry out the assignment rint-0＝|rk+1,Δt|，vint＝vk+1,ΔtAnd (3) ending the step (2); if Δ ferr,k+1,Δt|>εfThen proceed toAssignment rk＝rk+1,Δt，vk＝vk+1,ΔtAnd returns to (2.5) to continue execution.
(3) Iterative integral endpoint velocity vector
Comparing the distance between the earth and the heart | rnowI and rint-0If the difference between the two is larger, the speed of the re-entering point is continuously adjusted until the difference between the two is within the allowable range, and an integrated end point speed vector v is outputR＝vint-0. The specific implementation process is as follows:
(3.1) setting εrIs the geocentric distance threshold, if | | | rnow|-rint-0|≤εrThen, an integrated end point velocity vector v is outputR＝vint-0And (4) ending the step (3); if rnow|-rint-0|>εrThen, for | vBack-IterationI, disturbance is carried out on the value of delta v, and the value of | v is reassignedBack-Iteration|＝|vBack-IterationL + delta v, and step (2) is executed once again to obtain the integral geocentric distance r of the current positionint-0'. For the current integral ground center distance rint-ΔvAssignment, rint-Δv＝rint-0'。
(3.2) mixing | vBack-IterationThe re-assignment of the value is,
Figure BDA0002733642900000081
and returning to the step (2) to start execution.
(4) According to the current velocity vector vnowAnd the integrated end point velocity vector v obtained in step (3)RObtaining a gain velocity vector vgain＝vR-vnow。
(5) Let εvIs the velocity threshold, if | vgain|>εvThen output the thrust direction
Figure BDA0002733642900000082
If | vgain|≤εvAnd if so, the engine is shut down, and the off-track guidance is finished.
Parts of the invention not described in detail are common general knowledge to a person skilled in the art.

Claims (7)

1. A high-precision off-orbit reverse iterative guidance method is characterized by comprising the following steps:
(1) according to the current position vector rnowAnd a nominal reentry velocity vector veCalculating to obtain a flight range angle to be flown, a nominal speed and a nominal reentry speed direction vector;
(2) at a reentry velocity of magnitude | vBack-IterationI is an iteration initial value, and is reversely integrated from a re-entry point to a to-be-flown flight range angle delta fnowObtaining the integral earth-center distance r of the current positionint-0And vintAn integrated velocity vector for the current position;
(3) iteratively integrating the endpoint velocity vector;
(4) according to the current velocity vector vnowAnd the integrated end point velocity vector v obtained in step (3)RObtaining a gain velocity vector vgain＝vR-vnow；
(5) Let εvIs the velocity threshold, if | vgain|>εvThen the thrust direction is output outwards
Figure FDA0002733642890000011
If | vgain|≤εvAnd if so, the engine is shut down, and the off-track guidance is finished.
2. The high-precision off-orbit reverse iterative guidance method according to claim 1, characterized in that: the specific method of the step (1) comprises the following steps: according to the current position vector rnowRe-entering point position vector reAnd calculating to obtain the flight range angle to be flown
Figure FDA0002733642890000012
According to the nominal reentry velocity vector veObtaining a nominal velocity ve＝|ve| and nominal reentry velocity direction vector
Figure FDA0002733642890000013
3. The high-precision off-orbit reverse iterative guidance method according to claim 2, characterized in that: the specific method of the step (2) is as follows:
(2.1) reentry velocity magnitude | v at first calculationBack-IterationSelecting nominal speed ve(ii) a Then time-counting reentry velocity magnitude | vBack-IterationI is determined by the step (3);
(2.2) integrating the step number k and determining the reentry point position vector reIs assigned to rkThe reentry point velocity vector | vBack-Iteration|·ventry_unitAssign to vkI.e. rk＝re,vk＝|vBack-Iteration|·ventry_unit(ii) a Calculating the re-entry point to the inverse integral tkVoyage angle of time
Figure FDA0002733642890000021
Then calculate to obtain tkRemaining flight range angle delta f of timeerr,k＝Δfnow-Δft,k；
(2.3) integrating the position vector and the velocity vector by one step (k +1) to obtain an integral value r of the position vector and the velocity vectork+1,vk+1Calculating the re-entry point to the inverse integral tk+1Voyage angle of time
Figure FDA0002733642890000022
And then calculate tk+1Time residual flight distance angle delta ferr,k+1＝Δfnow-Δft,k+1；
(2.4) if Δ ferr,k·Δferr,k+1R is reassigned if the value is greater than or equal to 0k＝rk+1，vk＝vk+1，Δferr,k＝Δferr,k+1(ii) a And returning to the step (2.3) for re-execution; if Δ ferr,k·Δferr,k+1If the value is less than 0, entering the step (2.5);
(2.5) inverse integration time t as tIterationInitial value of (d), for tIterationDisturbance is carried out by delta t, and t is reassignedIteration＝tIteration+Δt；
(2.6) integrating the position vector r in the delta t direction by one step by using an integrator to obtain a position vector rΔtAnd velocity vector v ΔtCalculating to obtain the re-entry point to the inverse integral tIterationVoyage angle of time
Figure FDA0002733642890000023
Further calculating to obtain a residual flight range angle delta f to be flown at the moment of disturbance delta terr,Δt＝Δfnow-Δft,Δt；
(2.7) reassigning the at,
Figure FDA0002733642890000024
will tIterationReassign value, tIteration＝tIteration+Δt；
(2.8) integrating the position vector r in the delta t direction by one step by using an integrator to obtain a position vector rk+1,ΔtAnd velocity vector vk+1,ΔtCalculating to obtain the re-entry point to the inverse integral tIterationVoyage angle of time
Figure FDA0002733642890000025
Further calculating to obtain the residual flight range angle delta f at the time of the disturbance delta terr,k+1,Δt＝Δfnow-Δft,k+1,Δt；
(2.9) setting εfIs a range angle threshold, rint-0Is the integral geocentric distance, v, of the current positionintAn integrated velocity vector for the current position; if Δ ferr,k+1,Δt|≤εfThen carry out the assignment rint-0＝|rk+1,Δt|，vint＝vk+1,ΔtAnd entering the step (3); if Δ ferr,k+1,Δt|>εfThen carry out the assignment rk＝rk+1,Δt，vk＝vk+1,ΔtAnd returning to the step (2.5).
4. The high-precision off-orbit reverse iterative guidance method according to claim 3, characterized in that: the step change of the embedded Donman-Prince pair is used in the step (2.3)Long Runge-Kutta method DP5(4)7M integrator integrates forward by one step (k +1) to obtain integral value r of position vector and speed vectork+1,vk+1。
5. The high-precision off-orbit reverse iterative guidance method according to claim 3, characterized in that: in the step (2.6), a 4-order Runge-Kutta integrator is used for integrating one step in the delta t direction.
6. The high-precision off-orbit reverse iterative guidance method according to claim 3, characterized in that: the method of the step (3) comprises the following steps: comparing the distance between the earth and the heart | rnowI and rint-0If the difference between the two is larger, the speed of the re-entering point is continuously adjusted until the difference between the two is within the allowable range, and an integrated end point speed vector v is outputR＝vint-0。
7. The high-precision off-orbit reverse iterative guidance method according to claim 6, characterized in that: the specific implementation process of the step (3) is as follows:
(3.1) setting εrIs the geocentric distance threshold, if | | | rnow|-rint-0|≤εrThen, an integrated end point velocity vector v is outputR＝vint-0Entering the step (4); if rnow|-rint-0|>εrThen, for | vBack-IterationI, disturbance is carried out on the value of delta v, and the value of | v is reassignedBack-Iteration|＝|vBack-IterationL + delta v, and executing the step (2) once to obtain the integral earth-center distance r of the current positionint-0'; for the current integral ground center distance rint-ΔvAssignment, rint-Δv＝rint-0'；
(3.2) mixing | vBack-IterationThe re-assignment of the value is,
Figure FDA0002733642890000031
and returning to the step (2).
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