CN115494727A - Carrier rocket orbit-entering trajectory planning method based on orbit prediction - Google Patents

Carrier rocket orbit-entering trajectory planning method based on orbit prediction Download PDF

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CN115494727A
CN115494727A CN202210972843.2A CN202210972843A CN115494727A CN 115494727 A CN115494727 A CN 115494727A CN 202210972843 A CN202210972843 A CN 202210972843A CN 115494727 A CN115494727 A CN 115494727A
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orbit
carrier rocket
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张冉
李惠峰
郝泽明
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Beihang University
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Abstract

The invention provides a carrier rocket orbit entering track planning method based on track prediction, which comprises the following specific steps: 1. establishing a carrying goods shelf in-orbit flight problem model based on the track forecast; 2. establishing a convex optimization sub-problem of carrier rocket in-orbit; 3. and giving an initial guess and iteratively solving the carrier rocket orbital convex optimization subproblem. Through the steps, the method can realize the planning of the orbit entering track of the carrier rocket, can be applied on line, achieves better stability and universality, is scientific and good in manufacturability, and has wide popularization and application values.

Description

Carrier rocket orbit-entering trajectory planning method based on orbit prediction
Technical Field
The invention provides a carrier rocket orbit entering trajectory planning method based on orbit prediction, which is a trajectory planning method for a carrier rocket to be pushed into orbit through pushing and sliding in vacuum and belongs to aerospace; guidance, navigation and control techniques; the field of trajectory planning.
Background
In recent years, the human demand for obtaining space resources is increasing, so that the launching tasks of the carrier rocket are increasing; when a carrier rocket flies in space, a plurality of uncertainties can be faced, and the carrier rocket needs to have a track planning capability to ensure that normal orbit entering enters a preset orbit or enter a degraded orbit in case of failure;
in actual flight, the launch vehicle is generally propelled into a predetermined trajectory by a thrust; aiming at the form of pushing and sliding into the orbit, the current method mainly focuses on solving an optimal pushing and sliding sequence off line and planning a single full-pushing sequence on line according to a real-time state; this method requires a lot of off-line task design work and is difficult to cope with large deviations and failure situations during flight; therefore, researching a carrier rocket orbit-entering trajectory planning method capable of adapting to pushing, sliding and pushing becomes a key and difficult problem of research in the aerospace field;
in summary, in order to solve the problem of planning the orbit-entering trajectory of the existing carrier rocket, the invention mathematically describes the flight of the gliding section based on the trajectory forecast, and designs a trajectory planning method for the sliding-pushing flight.
Disclosure of Invention
Objects of the invention
The invention provides a carrier rocket orbit-entering trajectory planning method based on orbit prediction, aiming at an orbit-entering flight task in a vacuum environment, the gliding section flight is difficult to optimize due to the orbit-entering flight mode of push-slide push, so that the gliding section flight of a carrier rocket is described based on the orbit prediction, and the trajectory planning method is researched to solve the problems of poor universality, difficulty in on-line and the like in the prior art.
(II) technical scheme
The invention relates to a carrier rocket orbit-entering track planning method based on orbit prediction, which comprises the following specific steps:
firstly, establishing a carrying goods shelf in-orbit flight problem model based on track forecast;
determining a push-sliding-push flight mode of carrier rocket in-orbit flight according to task requirements, describing the flight of a sliding section by adopting an orbit forecasting formula, and establishing an optimal control problem model of carrier rocket in-orbit;
step two, establishing a carrier rocket orbital convex optimization sub-problem;
converting the carrier rocket in-orbit optimal control problem model established in the step one into a carrier rocket in-orbit convex optimization subproblem by a linearization method;
step three, giving an initial guess and iteratively solving a carrier rocket orbital convex optimization subproblem;
the step one is that the 'push-slide-push flight mode' refers to the flight time of two full push sections and the flight time of a gliding section in the process of the carrier rocket in-orbit flight;
wherein, the "orbit prediction formula" in the step one is:
Figure BDA0003797504940000021
in the formula r 0 And v 0 Respectively, the position, speed, r, of the starting moment of the gliding section c And v c Respectively the position and the speed of the starting moment of the taxiing section, mu is an earth gravity constant, and beta is the flight time of the normalized taxiing section;
wherein, the 'optimum control problem model for launching the carrier rocket in orbit' in the step one is as follows:
min-γκ 2
Figure BDA0003797504940000031
Figure BDA0003797504940000032
Figure BDA0003797504940000033
Figure BDA0003797504940000034
Figure BDA0003797504940000035
r 1 (t 1,f )＝r 0 ,v 1 (t 1,f )＝v 0 ,r 2 (t 2,0 )＝r c ,v 2 (t 2,0 )＝v c
Figure BDA0003797504940000036
Figure BDA0003797504940000037
in the formula r l And v l The position, the speed u of the carrier rocket in the full thrust section are respectively l Thrust acceleration of the carrier rocket in the full thrust section, a l Maximum thrust acceleration allowed for full thrust rocket, g l Is the gravitational acceleration, t, suffered by the full-thrust rocket 1,0 And t 2,0 Respectively, the starting flight times, t, of the two full push sections 1,f And t 2,f Flight times of two full push segments, h, respectively 1,f And h 2,f Respectively are normal vectors of the orbit plane where the two full-push-section terminal carrier rockets are positioned, h 1,set And h 2,set The normal vectors of the orbit planes, kappa, corresponding to two full-range terminals respectively given to the task 1 And kappa 2 The momentum moment vector module values, L, of two full-thrust terminal carrier rockets are respectively 1,f And L 2,f Are two full push segment terminal launch vehicle Laplacian vectors, L 1,set And L 2,set Laplace vectors r corresponding to two full-push-segment terminals respectively given to tasks p The current state of the carrier rocket corresponds to the altitude of the orbit at the near place, r p,set Given a terminal approximate height, r, for a task 1,0 And v 1,0 The initial position and the speed of the carrier rocket are obtained, and gamma is a penalty factor;
wherein, the linearization method in the step two is a classical method in the planning of the trajectory of the carrier rocket;
wherein, the 'carrier rocket orbital convex optimization subproblem' in the step two is as follows:
Figure BDA0003797504940000041
in the formula N l Number of discrete points, x, corresponding to two full push segments l,k ,l＝1,2,k＝1,…,N l +1 is the state of two full-thrust carrier rockets, x c And x c Respectively the states of the gliding section carrier rocket,
Figure BDA0003797504940000042
for initial guess, F is the virtual control variable, γ 1 、γ 2 、γ 3 For penalty factor, eta is a neighborhood operator, C, D, H x,1 、H x,2 、L x,1 、L x,2 、H 1 、H 2 、L 1 、L 2 、R x,2 R is a linearization parameter generated by a linearization process, A l 、B l,1 、B l,2 Is a state transition matrix;
wherein the "initial guess" in step three is a guess x of the terminal states of the two full-thrust segments and the gliding segment of the launch vehicle l 0 L =0,1,2, and the gravity acceleration sequence g l ；
Wherein, the "iterative solution" described in step three means that: solving the carrier rocket orbital convex optimization subproblem according to the initial guess, taking the solved result as the initial guess of the next solving, and stopping solving when the deviation between the solved result and the initial guess is less than the allowable error; according to the experience, the tolerance error is 0.0001-0.00001;
through the steps, the carrier rocket orbit-entering trajectory planning can be realized, the method can be applied on line, good stability and universality are achieved, and the method is scientific, good in manufacturability and wide in popularization and application value.
(III) the advantages and effects of the invention
(1) The method is based on the orbit prediction formula, can describe the gliding section flight of the carrier rocket, can meet the terminal orbit constraint given by a task, and can be used online;
(2) The method of the invention is scientific, has good manufacturability and has wide popularization and application value.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic view of the flight trajectory of a launch vehicle in an embodiment of the invention.
FIG. 3 is a schematic illustration of the results of launch vehicle control in an embodiment of the invention.
Detailed Description
The invention will be further explained in detail with reference to the drawings and the embodiments.
The invention relates to a planning method of an orbit entering track of a carrier rocket based on orbit prediction, a flow chart of which is shown in figure 1, and the method comprises the following steps:
firstly, establishing a carrying goods shelf in-orbit flight problem model based on track forecast;
determining the flight time t of the first full-push section of the carrier rocket according to task requirements 1,set Time of flight t of the second full push segment 2,set Normalized time of flight beta of taxis set And describing the taxiing section flight by adopting a track forecasting formula:
Figure BDA0003797504940000051
in the formula r 0 And v 0 Respectively the position, speed, r, of the starting moment of the gliding section c And v c Respectively the position and the speed of the starting moment of the gliding section, and mu is an earth gravity constant; according to the orbit forecasting formula, establishing a carrier rocket in-orbit optimal control problem model:
min-γκ 2
Figure BDA0003797504940000061
Figure BDA0003797504940000062
Figure BDA0003797504940000063
Figure BDA0003797504940000064
Figure BDA0003797504940000065
r 1 (t 1,set )＝r 0 ,v 1 (t 1,set )＝v 0 ,r 2 (t 2,0 )＝r c ,v 2 (t 2,0 )＝v c
Figure BDA0003797504940000066
Figure BDA0003797504940000067
in the formula r l And v l Respectively the position, the speed u of the carrier rocket in the full-thrust section l Thrust acceleration of the carrier rocket in the full thrust section, a l Maximum thrust acceleration allowed for full thrust rocket, g l Is the gravitational acceleration, t, borne by the full-thrust rocket 1,0 And t 2,0 Respectively, the starting flight times of the two full push sections, h 1,f And h 2,f Respectively are normal vectors of the orbital planes, h, of the two full-push-section terminal carrier rockets 1,set And h 2,set Orbit plane normal vectors, kappa, corresponding to two full-segment terminals respectively given to the task 1 And kappa 2 Momentum of two full-thrust-section terminal carrier rockets respectivelyMoment vector norm, L 1,f And L 2,f Are two full push segment terminal launch vehicle Laplacian vectors, L 1,set And L 2,set Laplace vectors, r, corresponding to two full-push terminals respectively given to the task p The current state of the carrier rocket corresponds to the altitude of the orbit at the near place, r p,set Given a terminal approximate height, r, for a task 1,0 And v 1,0 The initial position and the speed of the carrier rocket are obtained, and gamma is a penalty factor;
step two, establishing a carrier rocket orbital convex optimization sub-problem;
converting the carrier rocket in-orbit optimal control problem model established in the step one into a carrier rocket in-orbit convex optimization subproblem by a linearization method:
Figure BDA0003797504940000071
in the formula N l Number of discrete points corresponding to two full push segments, x l,k ,l＝1,2,k＝1,…,N l +1 is the state of two full-thrust carrier rockets, x c And x c Respectively the states of the gliding section carrier rocket,
Figure BDA0003797504940000072
for initial guess, F is the virtual control variable, γ 1 、γ 2 、γ 3 For penalty factor, eta is a neighborhood operator, C, D, H x,1 、H x,2 、L x,1 、L x,2 、H 1 、H 2 、L 1 、L 2 、R x,2 R is a linearization parameter generated by a linearization process, A l 、B l,1 、B l,2 The state transition matrix is calculated as follows:
Figure BDA0003797504940000073
step three, giving an initial guess, and iteratively solving a carrier rocket orbital convex optimization subproblem;
giving initial guess, and setting the terminal states x of two full-thrust sections and two gliding sections of the carrier rocket l 0,l =0,1,2 and the gravity acceleration sequence g l Guessing; when the gravity acceleration sequence is solved for the first time, the following method is adopted for calculation:
Figure BDA0003797504940000074
in the second and subsequent solving, the gravity acceleration sequence is calculated in the following way:
Figure BDA0003797504940000075
in the formula r l,j j =1, \8230, wherein N +1 is the position state of the carrier rocket obtained by solving the problem of the carrier rocket in-orbit convex optimization subproblem at the last time; defining:
Figure BDA0003797504940000081
solving the convex optimization subproblem of the carrier rocket in orbit according to the initial guess, and solving the result X * As initial guess X for the next solution 0 When | | | X * -X 0 Stopping solving when | | is less than or equal to epsilon;
simulation case:
the part takes a numerical simulation case as a method for demonstration, and is not an actual flight task;
dimensionless initial state of the launch vehicle is x 1,0 ＝[-0.7528,0.6346,0.3070,-0.6431,-0.6920,-0.1483] T The dimensionless flight time of the first full-push segment is t 1,set =0.0872, dimensionless flight time of the second full push segment t 1,set =0.8394, normalized time of flight for taxis β set =0.491, number of discrete points is N 1 ＝50,N 2 =100, thrust acceleration sequence is:
a 1,j ＝0.327/(1-0.327/0.556×0.0017×(j-1)),j＝1,…,51
a 2,j ＝0.327/(0.9488-0.327/0.556×0.0084×(j-1)),j＝1,…,101
the first iteration to solve a given dimensionless initial guess is:
Figure BDA0003797504940000082
according to the implementation process of the method, the schematic diagram of the flight path of the carrier rocket is shown in fig. 2, and the schematic diagram of the control result of the carrier rocket is shown in fig. 3.

Claims (6)

1. A carrier rocket orbit entering trajectory planning method based on orbit prediction is characterized by comprising the following specific steps:
step one, establishing a loading goods shelf in-orbit flight problem model based on track forecast;
determining a push-sliding-push flight mode of carrier rocket in-orbit flight according to task requirements, describing the flight of a sliding section by adopting an orbit forecasting formula, and establishing an optimal control problem model of carrier rocket in-orbit;
step two, establishing a carrier rocket orbital convex optimization sub-problem;
converting the carrier rocket in-orbit optimal control problem model established in the step one into a carrier rocket in-orbit convex optimization subproblem through a linearization method;
and step three, giving an initial guess and iteratively solving the carrier rocket orbital convex optimization subproblem.
2. The method of claim 1, wherein the method comprises: the 'push-slide-push flight mode' in the step one is the flight time of two full push sections and the flight time of a gliding section in the process of the carrier rocket in-orbit flight;
the "orbit prediction formula" in step one is:
Figure FDA0003797504930000011
in the formula r 0 And v 0 Respectively the position, speed, r, of the starting moment of the gliding section c And v c The position and the speed of the starting moment of the taxiing section are respectively, mu is an earth gravitational constant, and beta is the flight time of the normalized taxiing section.
3. The method of claim 1, wherein the method comprises: the 'optimal control problem model for launching the carrier rocket in orbit' in the step one is as follows:
min-γκ 2
Figure FDA0003797504930000021
Figure FDA0003797504930000022
Figure FDA0003797504930000023
Figure FDA0003797504930000024
Figure FDA0003797504930000025
r 1 (t 1,f )＝r 0 ,v 1 (t 1,f )＝v 0 ,r 2 (t 2,0 )＝r c ,v 2 (t 2,0 )＝v c
Figure FDA0003797504930000026
Figure FDA0003797504930000027
h 1,f ＝h 1,set ,L 1,f ＝L 1,set ,h 2,f ＝h 2,set ,L 2,f ＝L 2,set ,r p (t 2,f )＝r p,set (2)
r 1 (t 1,0 )＝r 1,0 ,v 1 (t 1,0 )＝v 1,0
in the formula r l And v l Respectively the position, the speed u of the carrier rocket in the full-thrust section l Thrust acceleration of the carrier rocket in the full thrust section, a l Maximum thrust acceleration allowed for full thrust rocket, g l Is the gravitational acceleration, t, suffered by the full-thrust rocket 1,0 And t 2,0 Respectively, the starting flight times, t, of the two full push sections 1,f And t 2,f Flight times, h, of two full push segments, respectively 1,f And h 2,f Respectively are normal vectors of the orbit plane where the two full-push-section terminal carrier rockets are positioned, h 1,set And h 2,set Orbit plane normal vectors, kappa, corresponding to two full-segment terminals respectively given to the task 1 And kappa 2 Respectively the momentum moment vector module values, L, of two full-thrust terminal carrier rockets 1,f And L 2,f Are two full-push terminal launch vehicles Laplacian vectors, L 1,set And L 2,set Laplace vectors r corresponding to two full-push-segment terminals respectively given to tasks p The current state of the carrier rocket corresponds to the perigee height of the orbit, r p,set Given a terminal approximate height, r, for a task 1,0 And v 1,0 Gamma is a penalty factor for the initial position and velocity of the carrier rocket.
4. The method of claim 1, wherein the method comprises: the 'convex optimization subproblem of launching vehicle into orbit' in the step two is as follows:
Figure FDA0003797504930000031
in the formula N l Number of discrete points, x, corresponding to two full push segments l,k ,l＝1,2,k＝1,…,N l +1 is the state of two full-thrust carrier rockets, x c And x c Respectively the states of the gliding section carrier rocket,
Figure FDA0003797504930000032
for initial guess, F is the virtual control variable, γ 1 、γ 2 、γ 3 For the penalty factor, eta is the proximity operator, C, D, H x,1 、H x,2 、L x,1 、L x,2 、H 1 、H 2 、L 1 、L 2 、R x,2 R is a linearization parameter generated by a linearization process, A l 、B l,1 、B l,2 Is a state transition matrix.
5. A method for planning the orbit of a launch vehicle based on orbit prediction according to claim 1 or 4, characterized in that: the "initial guess" in step three is a guess of the terminal states of the two full propulsion and taxiing sections of the launch vehicle
Figure FDA0003797504930000033
And a gravity acceleration sequence g l 。
6. The method for planning the orbit of the launch vehicle based on orbit prediction as claimed in claim 1, wherein the method comprises the following steps: the "iterative solution" described in step three means that: solving the carrier rocket orbital convex optimization subproblem according to the initial guess, taking a solving result as the initial guess of the next solving, and stopping solving when the deviation between the solving result and the initial guess is less than an allowable error; the tolerance is 0.0001-0.00001.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117687306A (en) * 2024-02-01 2024-03-12 北京航空航天大学 Five-in-one rocket track optimization method and system based on mode selection parameters

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117687306A (en) * 2024-02-01 2024-03-12 北京航空航天大学 Five-in-one rocket track optimization method and system based on mode selection parameters
CN117687306B (en) * 2024-02-01 2024-04-26 北京航空航天大学 Five-in-one rocket track optimization method and system based on mode selection parameters

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