CN113189870A - Trajectory re-planning method for elliptical rescue orbit under rocket thrust descent fault - Google Patents

Trajectory re-planning method for elliptical rescue orbit under rocket thrust descent fault Download PDF

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CN113189870A
CN113189870A CN202110388335.5A CN202110388335A CN113189870A CN 113189870 A CN113189870 A CN 113189870A CN 202110388335 A CN202110388335 A CN 202110388335A CN 113189870 A CN113189870 A CN 113189870A
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track
rescue
orbit
elliptical
fault
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何骁
谭述君
刘玉玺
毛玉明
吴志刚
张立勇
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Dalian University of Technology
Shanghai Aerospace System Engineering Institute
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Shanghai Aerospace System Engineering Institute
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention discloses a trajectory re-planning method of an elliptical rescue orbit under a rocket thrust descent fault, which comprises the following steps: constructing a track optimization problem of the elliptical rescue track under various thrust descent faults; solving the track optimization problem of the elliptical rescue track off-line by adopting a self-adaptive pseudo-spectrum method to obtain a sample set of fault state-orbit entering parameters; carrying out normalization processing on the sample data by adopting a maximum and minimum method, selecting a radial basis function network data center by adopting an orthogonal least square method, wherein the radial basis function is a Gaussian basis function, and training the radial basis function network in an off-line manner so as to establish a nonlinear mapping relation from a fault state to an orbit entry parameter; and solving the optimal propellant optimization problem on line by adopting a self-adaptive pseudo-spectrum method to obtain the flight trajectory. The method provides a reasonable initial value for the trajectory planning of the online elliptical rescue orbit through the radial basis function neural network decision-making orbit-entering parameter, and can avoid the reduction of the calculation efficiency caused by the conflict among variables in the objective function.

Description

Trajectory re-planning method for elliptical rescue orbit under rocket thrust descent fault
Technical Field
The invention relates to the technical field of rescue of a carrier rocket under a fault, in particular to a trajectory re-planning method of an elliptical rescue orbit under the fault of rocket thrust descent.
Background
The engine is used as a rocket power device and is a determining factor of the flight reliability and safety of the whole rocket. In an actual flight task, thrust is easy to drop due to reasons such as faults of a carrier rocket engine, and if a guidance control scheme under a nominal ballistic condition is continuously used, the task is difficult to complete, and the flight task fails.
In general, the trajectory optimization problem is described as an optimal control problem, and an adaptive pseudo-spectral method is widely applied in the traditional solving method. However, using only adaptive pseudo-spectroscopy has some disadvantages in solving the online trajectory optimization problem of thrust droop failure. First, improper setting of the initial values of the online trajectory optimization problem may result in long time-consuming or non-convergence of the adaptive pseudo-spectral solution. Secondly, contradictions between the orbital elements in the objective function can cause the search direction to diverge or the search step size to decrease, thereby reducing the feasibility of online application.
Disclosure of Invention
Aiming at the defect that the self-adaptive pseudo-spectrum method is long in time consumption or not converged in the online trajectory re-planning of the thrust descent fault, the invention provides the trajectory re-planning method, which provides a reasonable initial value for the trajectory planning of the online elliptical rescue orbit and can avoid the reduction of the calculation efficiency caused by the conflict among variables in the objective function.
In order to achieve the purpose, the technical scheme of the application is as follows: a trajectory re-planning method for an elliptical rescue orbit under a rocket thrust descent fault comprises the following steps:
establishing a secondary flight dynamics equation of the ascension section of the rocket in a geocentric inertial coordinate system, setting boundary conditions and constraint conditions according to different fault moments and thrust descent percentages, and constructing a track optimization problem of the elliptical rescue orbit under various thrust descent faults;
the method comprises the steps of solving a track optimization problem of the elliptical rescue track in an off-line mode by adopting a self-adaptive pseudo-spectrum method to obtain a sample set of fault state-in-orbit parameters, wherein the input characteristics of the sample set are fault states, the fault states comprise thrust fault moments, thrust descending magnitude, position, speed and quality, the output characteristics of the sample set are in-orbit parameters, and the in-orbit parameters comprise track semi-major axis, eccentricity, track inclination, rising intersection point right ascension and control variables of a terminal;
normalizing the sample data by adopting a maximum and minimum method, normalizing all data to be between [ -1,1], selecting a radial basis function network data center by an orthogonal least square method, wherein the radial basis function is a Gaussian basis function, training the radial basis function network in an off-line manner, and establishing a nonlinear mapping relation from a fault state to an orbit entering parameter;
migrating the radial basis function neural network to the actual flight of the rocket, taking the fault state of the flight as input, and making an on-line decision on an orbit entering parameter by the radial basis function neural network; setting a reasonable initial guess value for the trajectory planning by using the decided rescue track number and the terminal control variable; and converting the track optimization problem of the elliptical rescue track into an optimal propellant optimization problem by using the decided rescue track number, and solving the optimal propellant optimization problem on line by using a self-adaptive pseudo-spectrum method to obtain the flight track.
Further, when the track optimization problem of the elliptical rescue track under various thrust descent faults is established:
let X1The axis points in the equatorial plane in the direction of the principal meridian of the moment of emission, Z1With axis directed normal to the equatorial plane to the north pole, Y1And (3) establishing a secondary flight dynamics equation of the ascending section of the rocket in the geocentric inertial coordinate system according to the axis meeting the right-hand rule as follows:
Figure BDA0003015855700000031
Figure BDA0003015855700000032
Figure BDA0003015855700000033
wherein r and v are respectively the position and velocity vector of the carrier rocket,
Figure BDA0003015855700000034
is the first derivative of r and is,
Figure BDA0003015855700000035
is the first derivative of v; mu is GM which is the gravity constant of the earth, G is the gravity constant, and M is the mass of the earth; m is the total mass of the rocket,
Figure BDA0003015855700000036
is the first derivative of m, IspIs the engine specific impulse of the rocket; u ═ ux,uy,uz]TIs the thrust unit vector component of the engine; when the engine is in failure, the proportion of the thrust reduction is eta, and the thrust magnitude is (1-eta) Tnom，TnomIs the engine nominal thrust; g0Is the acceleration of gravity;
under the condition of thrust descent fault, the specific impulse of the engine is unchanged, the second consumption of the propellant is reduced by eta, the total flight time exceeds the nominal flight time, and the moment when the thrust descent fault of the engine occurs is assumed to be t0The carrier rocket needs to be at t0The state of the moment is taken as a starting point to optimize the rescue track, so the starting point equation constraint condition is expressed as:
x(t0)＝x0 (4)
in the formula, x0Is the state of the starting point.
By mfRepresenting the total mass of the carrier rocket and payload after depletion of the remaining fuel, the radius of the earth being R0(ii) a Defining a minimum safe track height of hsafeThe terminal quality and height should satisfy:
m(tf)≥mf,hsafe≤r(tf)-R0 (5)
the thrust descending fault occurs, the type of the elliptic rescue track is adopted, and the height of the track is improved as much as possible while the plane of the track is adjusted; the trajectory optimization problem of the elliptical rescue orbit is described as follows:
Figure BDA0003015855700000041
where J is the optimization target, λa,λe,λi,λΩAs a weighting factor, hpfCorresponding to the height of the near point of the track,
Figure BDA0003015855700000042
is the height of the target track at the near location, tfIs the terminal time, af,if,ΩfRespectively a semi-major axis, an inclination angle and a rising intersection point right ascension of the orbit,
Figure BDA0003015855700000043
respectively is the semimajor axis, the inclination angle and the ascent point right ascension of the target orbit.
Further, a reasonable initial guess value is set for the trajectory planning, and specifically the method comprises the following steps: according to the fault state, the number of terminal tracks for decision-making rescue by adopting radial basis function neural network
Figure BDA0003015855700000044
And terminal control variable
Figure BDA0003015855700000045
Wherein the content of the first and second substances,
Figure BDA0003015855700000046
respectively a semi-major axis, an eccentricity, an inclination angle and a rising intersection right ascension of the terminal track; in the initial guess, the time vector is
Figure BDA0003015855700000047
The state vector is
Figure BDA0003015855700000048
Vector of control variable is
Figure BDA0003015855700000049
Figure BDA00030158557000000410
A guess of time of flight equal to the remaining propellant divided by the second consumption;
Figure BDA00030158557000000411
is the thrust unit vector component when the fault occurs;
Figure BDA00030158557000000412
deciding a value from the number of tracks at the point of entry
Figure BDA00030158557000000413
Obtaining; the included angle between the lifting point and the track entering point is the geocentric angle phikIt is used to approximate the right ascension of the right ascension.
Furthermore, when the optimal propellant optimization problem is solved on line by adopting a self-adaptive pseudo-spectrum method,
because the number of the rescue track is known, the track optimization problem of the elliptical rescue track is converted into the optimal propellant optimization problem:
Figure BDA0003015855700000051
the method comprises the following steps that delta is an item which avoids the problem that the optimal propellant optimization problem cannot be solved due to positive errors of a semi-major axis of a track decided by a radial basis function neural network; in order to eliminate the influence of the positive semi-major axis error on the online track optimization, the end constraint of the semi-major axis is set as
Figure BDA0003015855700000052
Due to the adoption of the technical scheme, the invention can obtain the following technical effects:
(1) the radial basis function neural network can well fit the nonlinear relation of fault state-orbit parameters, and can quickly decide the number of rescue tracks and terminal control variables on line.
(2) The number of the rescue tracks and the terminal control variable are decided, and a reasonable initial value is provided for the track planning of the online elliptical rescue track.
(3) The determined number of the rescue tracks converts the track optimization problem of the elliptical rescue track into the optimal propellant optimization problem, and the reduction of the calculation efficiency caused by the conflict among variables in the objective function is avoided.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a diagram of a general strategy for trajectory optimization in the present invention;
FIG. 2 is a velocity altitude plot of the present invention;
fig. 3 is a plot of altitude in the present invention.
Detailed Description
The embodiments of the present invention are implemented on the premise of the technical solution of the present invention, and detailed embodiments and specific operation procedures are given, but the scope of the present invention is not limited to the following embodiments.
The embodiment provides a trajectory re-planning method for an elliptical rescue orbit under a rocket thrust descent fault, which is described with reference to fig. 1 and specifically comprises the following implementation steps:
s1: let X1The axis points in the equatorial plane in the direction of the principal meridian of the moment of emission, Z1With axis directed normal to the equatorial plane to the north pole, Y1And (3) establishing a secondary flight dynamics equation of the ascending section of the rocket in the geocentric inertial coordinate system according to the axis meeting the right-hand rule as follows:
Figure BDA0003015855700000061
Figure BDA0003015855700000062
Figure BDA0003015855700000063
wherein r and v are position and velocity vector of the carrier rocket, mu is GM is the gravitational constant, m is the total mass of the rocket, IspIs the engine specific impulse of the rocket; u ═ ux,uy,uz]TIs the thrust unit vector component of the engine; when the engine is in failure, the proportion of the thrust reduction is eta, and the thrust magnitude is (1-eta) Tnom，TnomIs the engine nominal thrust.
Under the condition of thrust descent fault, the specific impulse of the engine is unchanged, the second consumption of the propellant is reduced by eta, the total flight time exceeds the nominal flight time, and the moment when the thrust descent fault of the engine occurs is assumed to be t0The carrier rocket needs to be at t0The state of the moment is taken as a starting point to optimize the rescue track, so the starting point equation constraint condition is expressed as:
x(t0)＝x0 (4)
in the formula, x0Is the state of the starting point.
By mfRepresenting the total mass of the carrier rocket and payload after depletion of the remaining fuel, the radius of the earth being R0(ii) a Defining a minimum safe track height of hsafeThe terminal quality and height should satisfy:
m(tf)≥mf,hsafe≤r(tf)-R0 (5)
the thrust descending fault occurs, the type of the elliptic rescue track is adopted, and the height of the track is improved as much as possible while the plane of the track is adjusted. The trajectory optimization problem for an elliptical rescue trajectory can be described as:
Figure BDA0003015855700000071
where J is the optimization target, λa,λe,λi,λΩAs a weighting factor, hpfCorresponding to the height of the near point of the track,
Figure BDA0003015855700000072
is the height of the target track at the near location, tfIs the terminal time, af,if,ΩfRespectively a semi-major axis, an inclination angle and a rising intersection point right ascension of the orbit,
Figure BDA0003015855700000073
respectively is the semimajor axis, the inclination angle and the ascent point right ascension of the target orbit.
S2: the method comprises the steps of solving a track optimization problem of the elliptical rescue track in an off-line mode by adopting a self-adaptive pseudo-spectrum method, and obtaining a sample set of fault state orbit-entering parameters, wherein the input characteristics of the sample set are fault states, the fault states comprise thrust fault moments, thrust descending magnitude, positions, speeds and quality, the output characteristics of the sample set are orbit-entering parameters, and the orbit-entering parameters comprise track semi-major axes, eccentricity, track inclination angles, ascending intersection points right ascension and control variables of terminals.
S3: in order to eliminate the difference of the magnitude of each dimension of data and avoid the problem that the prediction error is larger due to the larger difference of the magnitude of the input data and the output data, the data needs to be normalized. The data were normalized using the maximum-minimum method, normalizing all data to between [ -1,1 ]. Considering that the rocket-borne computer has many computing tasks, the rescue track decision-making occupies fewer computing resources as well as better. And (3) selecting the RBF network data center by adopting an orthogonal least square method, and establishing a nonlinear mapping relation of fault state-orbit parameters.
The hidden unit is activated by a base function, the invention adopts a Gaussian base function, and the output of the jth hidden layer is as follows:
Figure BDA0003015855700000081
Figure BDA0003015855700000082
is the ith input data, μjIs the basis function center, σ, of the hidden nodejIs the radial basis function expansion speed. The center of the basis function and the speed of expansion are determined by the training of the network. The output layer linearly combines the outputs of the radial basis function concealment layers to generate the desired output. The output of the kth node of the output layer is:
Figure BDA0003015855700000083
in the formula, wjkThe weight of the jth hidden layer neuron to the kth output neuron. To achieve a suitable approximation accuracy, the following parameters are determined by training: the number of hidden layer neurons, the center of each hidden layer neuron basis function, the weight that the radial basis function output passes to the summation layer.
S4: the rescue orbit decision model is applied in an online migration mode, the actual flying fault state is used as input, and the radial basis function neural network is adopted to decide the number of terminal orbits for rescue
Figure BDA0003015855700000084
And terminal control variable
Figure BDA0003015855700000085
Wherein the content of the first and second substances,
Figure BDA0003015855700000086
respectively a semi-major axis, an eccentricity, an inclination angle and a rising intersection right ascension of the terminal track; in the initial guess, the time vector is
Figure BDA0003015855700000087
The state vector is
Figure BDA0003015855700000088
Vector of control variable is
Figure BDA0003015855700000089
Figure BDA00030158557000000810
A guess of time of flight equal to the remaining propellant divided by the second consumption;
Figure BDA0003015855700000091
is the thrust unit vector component when the fault occurs;
Figure BDA0003015855700000092
deciding a value from the number of tracks at the point of entry
Figure BDA0003015855700000093
Obtaining; the included angle between the lifting point and the track entering point is the geocentric angle phikIt is used to approximate the right ascension of the right ascension.
The track optimization problem of the elliptical rescue track can be converted into the optimal propellant optimization problem due to the fact that the track number of the rescue track is known
Figure BDA0003015855700000094
And delta is an item which avoids the problem that the optimal propellant optimization problem cannot be solved due to the positive error of the semi-major axis of the track decided by the neural network. In order to eliminate the influence of the positive semi-major axis error on the online track optimization, the end constraint of the semi-major axis is set as
Figure BDA0003015855700000095
Example 1
The whole secondary flight phase of the carrier rocket is taken as a research object, and the parameters are from documents Z.Song, C.Wang, Q.Gong, Joint dynamic optimization of the target orbit and flight trajectory of a launch vehicle based on state-trigged indices, actaAstronaut, 174(2020)82-93. the fitting points used by the adaptive pseudo-spectroscopy are zero points of orthogonal Legendre polynomials. The state distribution of the faults established by the sample set is 0-378 s according to the occurrence time, and the step length is 0.5 s; the thrust reduction is 13% -50%, the step length is 0.25%, and 5330 elliptical rescue orbit type samples are obtained. In the sample set, 90% of the data was randomly drawn as a training set, and the remaining 10% of the data was drawn as a test set. The diffusion factor for radial basis function neural network training is 0.5, and the final trained hidden layer neuron number is 300. The absolute error of the semi-major axis decision is [ -1.5,1.5 [)]In km interval, the absolute error of eccentricity is [ -2 × 10-4,2×10-4]Interval, absolute error of track inclination angle is [ -2X 10 [)-3,6×10-3]The absolute error of the right ascension at the intersection of the liter is [ -5X 10 [)-3,1×10-2]Degree. Compared with the circular orbit rescue type, the elliptical orbit rescue type has larger semi-major axis decision error because the nonlinear relation between the fault state and the semi-major axis in the elliptical orbit rescue type is more complex.
The trajectory based on the in-orbit parameter decision method of the invention is consistent with the trajectory obtained by using the adaptive pseudo-spectrum method only, as shown in fig. 2, the velocity curve obtained by the method is superposed with the velocity curve obtained by the adaptive pseudo-spectrum method. And after 147.5s, the flight track is adjusted, the flight time is prolonged, and the effective load is ensured to enter the elliptical rescue track. As can be seen from fig. 3, the height of the track obtained by the method of the present invention is slightly lower than the height of the track obtained by the adaptive pseudo-spectrum method, which is caused by the introduction of the delta term. The calculation time of the online trajectory re-planning method provided by the invention is 98.8% less than that of the method only using the self-adaptive pseudo-spectrum method. The improvement in computational efficiency is mainly due to the tracking parameter decision. On one hand, the decided track entry parameter provides a proper reference value for setting an initial value; and on the other hand, the objective function is simplified, and the searching efficiency of the optimal solution is improved.
The embodiments of the present invention are illustrative, but not restrictive, of the invention in any manner. The technical features or combinations of technical features described in the embodiments of the present invention should not be considered as being isolated, and they may be combined with each other to achieve a better technical effect. The scope of the preferred embodiments of the present invention may also include additional implementations, and this should be understood by those skilled in the art to which the embodiments of the present invention pertain.

Claims (4)

1. A trajectory re-planning method for an elliptical rescue orbit under a rocket thrust descent fault is characterized by comprising the following steps:
establishing a secondary flight dynamics equation of the ascension section of the rocket in a geocentric inertial coordinate system, setting boundary conditions and constraint conditions according to different fault moments and thrust descent percentages, and constructing a track optimization problem of the elliptical rescue orbit under various thrust descent faults;
the method comprises the steps of solving a track optimization problem of the elliptical rescue track in an off-line mode by adopting a self-adaptive pseudo-spectrum method to obtain a sample set of fault state-in-orbit parameters, wherein the input characteristics of the sample set are fault states, the fault states comprise thrust fault moments, thrust descending magnitude, position, speed and quality, the output characteristics of the sample set are in-orbit parameters, and the in-orbit parameters comprise track semi-major axis, eccentricity, track inclination, rising intersection point right ascension and control variables of a terminal;
normalizing the sample data by adopting a maximum and minimum method, normalizing all data to be between [ -1,1], selecting a radial basis function network data center by an orthogonal least square method, wherein the radial basis function is a Gaussian basis function, training the radial basis function network in an off-line manner, and establishing a nonlinear mapping relation from a fault state to an orbit entering parameter;
migrating the radial basis function neural network to the actual flight of the rocket, taking the fault state of the flight as input, and making an on-line decision on an orbit entering parameter by the radial basis function neural network; setting a reasonable initial guess value for the trajectory planning by using the decided rescue track number and the terminal control variable; and converting the track optimization problem of the elliptical rescue track into an optimal propellant optimization problem by using the decided rescue track number, and solving the optimal propellant optimization problem on line by using a self-adaptive pseudo-spectrum method to obtain the flight track.
2. The trajectory re-planning method for the elliptical rescue orbit under the rocket thrust descent fault according to claim 1, characterized in that when a trajectory optimization problem for the elliptical rescue orbit under various thrust descent faults is constructed:
let X1The axis points in the equatorial plane in the direction of the principal meridian of the moment of emission, Z1With axis directed normal to the equatorial plane to the north pole, Y1And (3) establishing a secondary flight dynamics equation of the ascending section of the rocket in the geocentric inertial coordinate system according to the axis meeting the right-hand rule as follows:
Figure FDA0003015855690000021
Figure FDA0003015855690000022
Figure FDA0003015855690000023
wherein r and v are respectively the position and velocity vector of the carrier rocket,
Figure FDA0003015855690000024
is the first derivative of r and is,
Figure FDA0003015855690000025
is the first derivative of v; mu is GM which is the gravity constant of the earth, G is the gravity constant, and M is the mass of the earth; m is the total mass of the rocket,
Figure FDA0003015855690000026
is the first derivative of m, IspIs the engine specific impulse of the rocket; u ═ ux,uy,uz]TIs the thrust unit vector component of the engine; when the engine is in failure, the proportion of the thrust reduction is eta, and the thrust magnitude is (1-eta) Tnom，TnomIs the engine nominal thrust; g0Is gravity forceAcceleration;
under the condition of thrust descent fault, the specific impulse of the engine is unchanged, the second consumption of the propellant is reduced by eta, the total flight time exceeds the nominal flight time, and the moment when the thrust descent fault of the engine occurs is assumed to be t0The carrier rocket needs to be at t0The state of the moment is taken as a starting point to optimize the rescue track, so the starting point equation constraint condition is expressed as:
x(t0)＝x0 (4)
in the formula, x0Is the state of the starting point.
By mfRepresenting the total mass of the carrier rocket and payload after depletion of the remaining fuel, the radius of the earth being R0(ii) a Defining a minimum safe track height of hsafeThe terminal quality and height should satisfy:
m(tf)≥mf,hsafe≤r(tf)-R0 (5)
the thrust descending fault occurs, the type of the elliptic rescue track is adopted, and the height of the track is improved as much as possible while the plane of the track is adjusted; the trajectory optimization problem of the elliptical rescue orbit is described as follows:
Figure FDA0003015855690000031
where J is the optimization target, λa,λe,λi,λΩAs a weighting factor, hpfCorresponding to the height of the near point of the track,
Figure FDA0003015855690000032
is the height of the target track at the near location, tfIs the terminal time, af,if,ΩfRespectively a semi-major axis, an inclination angle and a rising intersection point right ascension of the orbit,
Figure FDA0003015855690000033
respectively is the semimajor axis, the inclination angle and the ascent point right ascension of the target orbit.
3. The trajectory re-planning method for the elliptical rescue orbit under the rocket thrust descent fault according to claim 1, characterized in that a reasonable initial guess value is set for trajectory planning, specifically: according to the fault state, the number of terminal tracks for decision-making rescue by adopting radial basis function neural network
Figure FDA0003015855690000034
And terminal control variable
Figure FDA0003015855690000035
Wherein the content of the first and second substances,
Figure FDA0003015855690000036
respectively a semi-major axis, an eccentricity, an inclination angle and a rising intersection right ascension of the terminal track; in the initial guess, the time vector is
Figure FDA0003015855690000037
The state vector is
Figure FDA0003015855690000038
Vector of control variable is
Figure FDA0003015855690000039
Figure FDA00030158556900000310
A guess of time of flight equal to the remaining propellant divided by the second consumption;
Figure FDA00030158556900000311
is the thrust unit vector component when the fault occurs;
Figure FDA00030158556900000312
deciding a value from the number of tracks at the point of entry
Figure FDA00030158556900000313
Obtaining; the included angle between the lifting point and the track entering point is the geocentric angle phikIt is used to approximate the right ascension of the right ascension.
4. The method for re-planning the trajectory of the elliptical rescue orbit under the rocket thrust descent fault according to claim 1, wherein when an optimal propellant optimization problem is solved on line by adopting a self-adaptive pseudo-spectrum method,
because the number of the rescue track is known, the track optimization problem of the elliptical rescue track is converted into the optimal propellant optimization problem:
Figure FDA0003015855690000041
the method comprises the following steps that delta is an item which avoids the problem that the optimal propellant optimization problem cannot be solved due to positive errors of a semi-major axis of a track decided by a radial basis function neural network; in order to eliminate the influence of the positive semi-major axis error on the online track optimization, the end constraint of the semi-major axis is set as
Figure FDA0003015855690000042
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CN114413691A (en) * 2021-12-24 2022-04-29 北京航天自动控制研究所 Cross-gliding-section analytic guidance reconstruction method for thrust descent fault of carrier rocket
CN114718762A (en) * 2022-05-18 2022-07-08 北京宇航系统工程研究所 High-thrust oxyhydrogen rocket engine shutdown method for improving rail-in probability
CN115230996A (en) * 2022-09-21 2022-10-25 北京星河动力装备科技有限公司 Method, device, system, electronic device and storage medium for controlling a last-stage of a stuck rail

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