CN111846288B - Small celestial body soft landing differential game control method in uncertain environment - Google Patents

Small celestial body soft landing differential game control method in uncertain environment Download PDF

Info

Publication number
CN111846288B
CN111846288B CN202010750835.4A CN202010750835A CN111846288B CN 111846288 B CN111846288 B CN 111846288B CN 202010750835 A CN202010750835 A CN 202010750835A CN 111846288 B CN111846288 B CN 111846288B
Authority
CN
China
Prior art keywords
lander
landing
celestial body
moving target
small celestial
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010750835.4A
Other languages
Chinese (zh)
Other versions
CN111846288A (en
Inventor
龙嘉腾
朱圣英
梁子璇
徐瑞
修文博
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Technology BIT
Original Assignee
Beijing Institute of Technology BIT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Technology BIT filed Critical Beijing Institute of Technology BIT
Priority to CN202010750835.4A priority Critical patent/CN111846288B/en
Publication of CN111846288A publication Critical patent/CN111846288A/en
Application granted granted Critical
Publication of CN111846288B publication Critical patent/CN111846288B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/62—Systems for re-entry into the earth's atmosphere; Retarding or landing devices
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Remote Sensing (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Mathematical Optimization (AREA)
  • Theoretical Computer Science (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Data Mining & Analysis (AREA)
  • Computational Mathematics (AREA)
  • Algebra (AREA)
  • General Engineering & Computer Science (AREA)
  • Software Systems (AREA)
  • Databases & Information Systems (AREA)
  • Operations Research (AREA)
  • Chemical & Material Sciences (AREA)
  • Combustion & Propulsion (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a small celestial body soft landing differential game control method in an uncertain environment, and belongs to the technical field of deep space exploration. The implementation method of the invention comprises the following steps: determining the movement form of the lander in the irregular weak gravitational field under the condition that the accurate gravitational field model of the target small celestial body is unknown, designing a virtual moving target landing point by adopting a state error propagation method, and converting the uncertain influence of the irregular gravitational field on the movement of the lander into random movement of the virtual moving target landing point; and designing an optimal landing control strategy of the lander based on the zero and random differential game, and controlling the lander to land according to the optimal landing control strategy, so that the landing precision of the lander at a preset position on the surface of the small celestial body is improved.

Description

Small celestial body soft landing differential game control method in uncertain environment
Technical Field
The invention relates to a landing control method, in particular to a small celestial body soft landing control method, and belongs to the technical field of deep space exploration.
Background
The precise soft landing of the surface of the small celestial body is a necessary premise for implementing tasks such as in-situ detection, sampling return and the like of the surface of the small celestial body. Because the small celestial body has small mass, the formed weak gravitation can not agglomerate the small celestial body into a sphere-like celestial body. Therefore, the small celestial bodies in the solar system have different shapes, so that the distribution of the gravitational field around the small celestial bodies is irregular, and accurate modeling is difficult.
Under the conditions that the gravitational field environment is extremely complex and unknown and accurate modeling is difficult, the control difficulty for realizing soft landing on the surface of the small celestial body is extremely high, and the requirement on the control accuracy is extremely high. In a weak gravitational field, the escape speed of the detector is very low, and a slight control error may cause the detector to collide when landing, so that bounce is generated and even the detector is caused to escape.
Considering the requirement of high-precision landing control of the small celestial body, the accurate landing of the lander on the surface of the small celestial body is realized by designing a corresponding lander control method under the condition that an accurate model of an irregular gravitational field of the small celestial body is unknown.
Disclosure of Invention
The invention discloses a small celestial body soft landing differential game control method in an uncertain environment, which aims to solve the technical problems that: under the condition that a target small celestial body accurate gravitational field model is unknown, a virtual moving target landing point is designed through a state error propagation method, the uncertain influence of an irregular gravitational field on the movement of a lander is converted into random movement of the virtual moving target landing point, then an optimal landing control strategy of the lander is designed through a zero and random differential game method, and the landing accuracy of the lander at a preset position on the surface of a small celestial body is improved.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a small celestial body soft landing differential game control method in an uncertain environment, which is used for determining the movement form of a lander in an irregular weak gravitational field, designing a virtual moving target landing point by adopting a state error propagation method and converting the uncertain influence of the irregular gravitational field on the lander movement into random movement of the virtual moving target landing point. And designing an optimal landing control strategy of the lander based on the zero and random differential game, and controlling the lander to land according to the optimal landing control strategy, so that the landing precision of the lander at a preset position on the surface of the small celestial body is improved.
The invention discloses a small celestial body soft landing differential game control method in an uncertain environment, which comprises the following steps:
step 1, determining the movement form of the lander in the irregular weak gravitational field.
To be provided with
Figure GDA0003197159260000011
For state variable, the detector is fixedly connected with a coordinate system at the center of the small celestial body
Figure GDA0003197159260000012
The kinetic equation below is
Figure GDA0003197159260000021
Wherein ω is [0,0, ω ═ o]TIs a planetary self-rotation angular velocity vector,
Figure GDA0003197159260000022
in order to be the acceleration vector of the local gravitational force,
Figure GDA0003197159260000023
the vector is controlled for the thrust of the probe,
Figure GDA0003197159260000024
is the magnitude of the thrust control vector and satisfies the condition that u is T/m, IspSpecific impulse of aircraft thruster, gEIs the acceleration of gravity at sea level of the earth, adFor unmodeled disturbances and obeying Gaussian white noise
Figure GDA0003197159260000025
Where q (t) is the spectral density and δ (t- τ) is the dirac function at t τ. The inner spherical harmonic function model of the small celestial body gravitation field is
Figure GDA0003197159260000026
Wherein GM and r are the gravitational constant and nominal radius of the small celestial body, PnmIs an associative Legendre polynomial, CnmAnd SnmIs the spherical harmonic coefficient, theta,
Figure GDA0003197159260000027
R is the longitude, the latitude and the radius of the position of the detector, and satisfies the relation shown in the formula.
Figure GDA0003197159260000028
In the small celestial body landing control problem, the following boundary constraints need to be satisfied
Figure GDA0003197159260000029
Wherein r is0And v0Respectively, the initial time t ═ t0Position and velocity vector of the detector, m0Is the quality of the detector at the initial moment; r isfAnd vfRespectively at landing time (t ═ t)f) Target position and velocity vector of the probe. During landing, the thrust amplitude of the detector needs to meet the following constraint
Tmin≤||T||≤Tmax (6)
Wherein, TminAnd TmaxRespectively the minimum value and the maximum value of the amplitude of the thruster. The dynamics equation determines the lander motion form in the irregular weak gravitational field and records the dynamics equation as
Figure GDA0003197159260000031
And 2, designing a virtual moving target landing point by adopting a state error propagation method, and converting the uncertain influence of the irregular gravitational field on the movement of the lander into random movement of the virtual moving target landing point.
The Fokker-Planck-Kolmogorov (FPK) equation in the formula describes the propagation process of the state error distribution function.
Figure GDA0003197159260000032
Wherein the probability density function p (x, t) of the state error is approximated by a gaussian mixture model.
Figure GDA0003197159260000033
Wherein, mui(t) and Pi(t) are Gaussian probability density functions N (x | mu) respectivelyi(t),Pi(t)) by linear covariance or by unscented variationThe method is also disclosed. The constraint condition that the weight coefficient needs to satisfy is determined by an equation.
Figure GDA0003197159260000034
Definition error
Figure GDA0003197159260000035
The weighting coefficients of the gaussian mixture model are obtained by solving the optimization problem given by the formula.
Figure GDA0003197159260000036
And solving to obtain a probability density function p (x, t) of the lander state error. Then at the end time the probability density function for the lander state error is p (x, t)f). Let random variables Δ (t) -p (x, t)f) Defining the state variable of the virtual target landing site as
Figure GDA0003197159260000037
The virtual moving target landing site motion is described as
Figure GDA0003197159260000038
Wherein the content of the first and second substances,
Figure GDA0003197159260000039
I 6×3＝[03×3,I3]. The motion of the virtual moving target landing site is determined by equation. And (3) designing a virtual moving target landing point by adopting a state error propagation method given by an FPK equation in the formula (8), and converting the uncertain influence of the irregular gravitational field on the movement of the lander into random movement of the virtual moving target landing point shown in the formula (13).
Step 3, based on zero and random microOptimal landing control strategy u of game-based design lander*And controlling the lander to land according to the optimal landing control strategy, so that the landing precision of the lander at the preset position of the surface of the small celestial body is improved.
The precise landing problem of the surface of the small celestial body is converted into the zero-escape pursuit and differential game problem by introducing a virtual moving target landing point, wherein the lander is a chaser, the motion of which is determined by a completely known kinetic equation, namely unmodeled disturbance ad0; the virtual moving target landing point is an escaper, and the motion of the virtual moving target landing point is determined by the formula. Order to
Figure GDA0003197159260000041
And satisfy
Figure GDA0003197159260000042
Wherein u isvAnd the virtual control quantity corresponding to the virtual moving target landing point. The performance index of the chase escape zero and differential game problem is defined as the time at the end of the game (t ═ t)f) The relative distance between the two parties is shown in the formula.
J＝||x(tf)-xt(tf)|| (15)
The optimal strategy for landers (chasers) is to minimize the relative distance between the two parties, while the optimal strategy for virtual moving target landing sites (escapes) is to maximize the relative distance between the two parties, i.e., to maximize the distance between the two parties
Figure GDA0003197159260000043
Thus, the catch-up and differential gaming problems are given by the equation. Solving through a saddle point planning method to obtain a control strategy u of a lander in an irregular gravitational field*。
Under the condition that the accurate gravitational field model of the target small celestial body is unknown, the landing accuracy of the lander at the preset position of the surface of the small celestial body is improved by designing a corresponding landing control strategy.
Has the advantages that:
1. the invention discloses a small celestial body soft landing differential game control method in an uncertain environment, which designs a virtual moving target landing point through a state error propagation method, converts the uncertain influence of an irregular gravitational field on the movement of a lander into the random movement of the virtual moving target landing point, realizes equivalent conversion of the modeling error of the irregular gravitational field of a small celestial body, and further facilitates the design of an optimal landing control strategy of the lander through a zero sum random differential game method.
2. The invention discloses a small celestial body soft landing differential game control method in an uncertain environment, which designs an optimal landing control strategy of a lander through a zero and random differential game method, and dynamically tracks a virtual moving target landing point by the lander, namely, the lander is controlled to land according to the optimal landing control strategy, and the landing precision of the lander at a preset position on the surface of a small celestial body is improved under the condition of gravitational field modeling error.
Drawings
FIG. 1 is a flow chart of a small celestial body soft landing differential game control method in an uncertain environment;
FIG. 2 is a plot of lander conditions over time.
Detailed Description
For a better understanding of the objects and advantages of the invention, reference is made to the following description, taken in conjunction with the accompanying drawings, which illustrate, by way of example, the principles of the invention.
As shown in fig. 1, the method for controlling a differential game of soft landing of a small celestial body in an uncertain environment disclosed in this embodiment includes the following steps:
step 1, determining the movement form of the lander in the irregular weak gravitational field.
To be provided with
Figure GDA0003197159260000051
For state variable, the detector is fixedly connected with a coordinate system at the center of the small celestial body
Figure GDA0003197159260000052
The kinetic equation below is
Figure GDA0003197159260000053
Wherein ω is [0,0, ω ═ o]TIs a planetary self-rotation angular velocity vector,
Figure GDA0003197159260000054
in order to be the acceleration vector of the local gravitational force,
Figure GDA0003197159260000055
the vector is controlled for the thrust of the probe,
Figure GDA0003197159260000056
is the magnitude of the thrust control vector and satisfies the condition that u is T/m, IspSpecific impulse of aircraft thruster, gEIs the acceleration of gravity at sea level of the earth, adFor unmodeled disturbances and obeying Gaussian white noise
Figure GDA0003197159260000057
Where q (t) is the spectral density and δ (t- τ) is the dirac function at t τ. The small celestial body Eros433 is used as a target celestial body, and the spherical harmonic function model in the small gravitational field is
Figure GDA0003197159260000058
Wherein GM is 446210m3/s2And r 16km is the gravity constant and nominal radius of the small celestial body Eros433, PnmIs an associative Legendre polynomial, CnmAnd SnmIs the spherical harmonic coefficient, theta,
Figure GDA0003197159260000059
R is the longitude, the latitude and the radius of the position of the detector, and satisfies the relation shown in the formula.
Figure GDA00031971592600000510
In the small celestial body landing control problem, the following boundary constraints need to be satisfied
Figure GDA00031971592600000511
Wherein r is0＝[10117,6956,8256]m and v0＝[-25,-12,-17]m/s is respectively the initial time t ═ t0Position and velocity vector of the detector, m0300kg is the mass of the probe at the initial moment; r isf＝[853,5010,45]m and vf＝[0,0,0]m/s is landing time (t ═ t)f) Target position and velocity vector of the probe. During landing, the thrust amplitude of the detector needs to meet the following constraint
Tmin≤||T||≤Tmax (22)
Wherein, Tmin2N and Tmax18N are the minimum and maximum values of the thruster amplitude, respectively. The dynamics equations determine the form of lander motion in the irregular weak gravitational field. Let the kinetic equation be
Figure GDA0003197159260000061
And 2, designing a virtual moving target landing point by adopting a state error propagation method, and converting the uncertain influence of the irregular gravitational field on the movement of the lander into random movement of the virtual moving target landing point.
The Fokker-Planck-Kolmogorov (FPK) equation in the formula describes the propagation process of the state error distribution function.
Figure GDA0003197159260000062
Wherein the probability density function p (x, t) of the state error is approximated by a gaussian mixture model.
Figure GDA0003197159260000063
Wherein, mui(t) and Pi(t) are Gaussian probability density functions N (x | mu) respectivelyi(t),Pi(t)) mean and covariance, obtained by linear covariance or unscented transformation methods. The constraint condition that the weight coefficient needs to satisfy is determined by an equation.
Figure GDA0003197159260000064
Definition error
Figure GDA0003197159260000065
The weighting coefficients of the gaussian mixture model are obtained by solving the optimization problem given by the formula.
Figure GDA0003197159260000066
And solving to obtain a probability density function p (x, t) of the lander state error. Then at the end time the probability density function for the lander state error is p (x, t)f). Let random variables Δ (t) -p (x, t)f) Defining the state variable of the virtual target landing site as xt(t)＝[rt T(t),vt T(t)]TThen the virtual moving target landing site motion is described as
Figure GDA0003197159260000071
Wherein the content of the first and second substances,
Figure GDA0003197159260000072
I 6×3＝[03×3,I3]. The motion of the virtual moving target landing site is determined by equation.
Step 3, designing optimal landing control strategy u of lander based on zero and random differential game*And controlling the lander to land according to the optimal landing control strategy, so that the landing precision of the lander at the preset position of the surface of the small celestial body is improved.
The precise landing problem of the surface of the small celestial body is converted into the zero-escape pursuit and differential game problem by introducing a virtual moving target landing point, wherein the lander is a chaser, the motion of which is determined by a completely known kinetic equation, namely unmodeled disturbance ad0; the virtual moving target landing point is an escaper, and the motion of the virtual moving target landing point is determined by the formula. Order to
Figure GDA0003197159260000075
And satisfy
Figure GDA0003197159260000073
Wherein u isvAnd the virtual control quantity corresponding to the virtual moving target landing point. The performance index of the chase escape zero and differential game problem is defined as the time at the end of the game (t ═ t)f) The relative distance between the two parties is shown in the formula.
J＝||x(tf)-xt(tf)|| (31)
The optimal strategy for landers (chasers) is to minimize the relative distance between the two parties, while the optimal strategy for virtual moving target landing sites (escapes) is to maximize the relative distance between the two parties, i.e., to maximize the distance between the two parties
Figure GDA0003197159260000074
Thus, the catch-up and differential gaming problems are given by the equation. Solving through a saddle point planning method to obtain a control strategy u of a lander in an irregular gravitational field*。
Under the condition that the accurate gravitational field model of the target small celestial body is unknown, the landing accuracy of the lander at the preset position of the surface of the small celestial body is improved by designing a corresponding landing control strategy.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (4)

1. The small celestial body soft landing differential game control method in the uncertain environment is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
step 1, determining a lander motion form in an irregular weak gravitational field;
step 2, designing a virtual moving target landing point by adopting a state error propagation method, and converting the uncertain influence of the irregular gravitational field on the movement of the lander into random movement of the virtual moving target landing point;
step 3, designing optimal landing control strategy u of lander based on zero and random differential game*And controlling the lander to land according to the optimal landing control strategy, and improving the landing precision of the lander at a preset position on the surface of the small celestial body.
2. The differential gaming control method for soft landing of celestial bodies in uncertain environments of claim 1, wherein: the step 1 is realized by the method that,
to be provided with
Figure FDA0003209077390000011
For state variable, the detector is fixedly connected with a coordinate system at the center of the small celestial body
Figure FDA0003209077390000012
The kinetic equation below is
Figure FDA0003209077390000013
Wherein ω is [0,0, ω ═ o]TIs a planetary self-rotation angular velocity vector,
Figure FDA0003209077390000014
in order to be the acceleration vector of the local gravitational force,
Figure FDA0003209077390000015
the vector is controlled for the thrust of the probe,
Figure FDA0003209077390000016
is the magnitude of the thrust control vector and satisfies the condition that u is T/m, IspSpecific impulse of aircraft thruster, gEIs the acceleration of gravity at sea level of the earth, adFor unmodeled disturbances and obeying Gaussian white noise
Figure FDA0003209077390000017
Where q (t) is the spectral density and δ (t- τ) is the dirac function at t ═ τ; the inner spherical harmonic function model of the small celestial body gravitation field is
Figure FDA0003209077390000018
Wherein GM and r are the gravitational constant and nominal radius of the small celestial body, PnmIs an associative Legendre polynomial, CnmAnd SnmIs the spherical harmonic coefficient, theta,
Figure FDA0003209077390000019
R is the longitude, latitude and radius of the position of the detector, and satisfies the relation shown in the formula
Figure FDA00032090773900000110
In the small celestial body landing control problem, the following boundary constraints need to be satisfied
Figure FDA0003209077390000021
Wherein r is0And v0Respectively, the initial time t ═ t0Position and velocity vector of the detector, m0Is the quality of the detector at the initial moment; r isfAnd vfRespectively at landing time (t ═ t)f) Target position and velocity vector of the probe; during landing, the thrust amplitude of the detector needs to meet the following constraint
Tmin≤||T||≤Tmax (6)
Wherein, TminAnd TmaxRespectively the minimum value and the maximum value of the amplitude of the thruster; the dynamics equation determines the lander motion form in the irregular weak gravitational field and records the dynamics equation as
Figure FDA0003209077390000022
3. The differential gaming control method for soft landing of celestial bodies in uncertain environments of claim 2, characterized by: the step 2 is realized by the method that,
the Fokker-Planck-Kolmogorov (FPK) equation in the formula describes the propagation process of a state error distribution function;
Figure FDA0003209077390000023
wherein the probability density function p (x, t) of the state error is approximated by a Gaussian mixed mode pattern;
Figure FDA0003209077390000024
wherein, mui(t) and Pi(t) are Gaussian probability density functions N (x | mu) respectivelyi(t),Pi(t)) means and covariance, obtained by linear covariance or unscented transformation; the constraint condition to be satisfied by the weight coefficient is determined by the formula
Figure FDA0003209077390000025
Definition error
Figure FDA0003209077390000026
The weight coefficients of the gaussian mixture model are obtained by solving the optimization problem given by the formula
Figure FDA0003209077390000031
Obtaining a probability density function p (x, t) of the lander state error through a solving formula; then at the end time the probability density function for the lander state error is p (x, t)f) (ii) a Let random variables Δ (t) -p (x, t)f) Defining the state variable of the virtual target landing site as
Figure FDA0003209077390000032
The virtual moving target landing site motion is described as
Figure FDA0003209077390000033
Wherein the content of the first and second substances,
Figure FDA0003209077390000034
I 6×3＝[03×3,I3](ii) a The motion of the virtual moving target landing site is determined by formula; and (3) designing a virtual moving target landing point by adopting a state error propagation method given by an FPK equation in the formula (8), and converting the uncertain influence of the irregular gravitational field on the movement of the lander into random movement of the virtual moving target landing point shown in the formula (13).
4. The differential gaming control method for soft landing of celestial bodies in uncertain environments of claim 3, wherein: the step 3 is realized by the method that,
the precise landing problem of the surface of the small celestial body is converted into the zero-escape pursuit and differential game problem by introducing a virtual moving target landing point, wherein the lander is a chaser, the motion of which is determined by a completely known kinetic equation, namely unmodeled disturbance ad0; the virtual moving target landing point is an escaper, and the motion of the virtual moving target landing point is determined by the formula; order to
Figure FDA0003209077390000035
And satisfy
Figure FDA0003209077390000036
Wherein u isvThe virtual control quantity corresponding to the virtual moving target landing point; the performance index of the chase escape zero and differential game problem is defined as the time at the end of the game (t ═ t)f) The relative distance between the two parties is shown as the formula
J＝||x(tf)-xt(tf)|| (15)
The optimal strategy of the lander is to minimize the relative distance between the two parties, while the optimal strategy of the virtual moving target landing point (escaper) is to maximize the relative distance between the two parties, i.e. the lander is a virtual moving target landing point
Figure FDA0003209077390000037
Thus, the catch-up and differential game problem is given by the equation; passing through the saddle pointSolving type control strategy u for obtaining lander in irregular gravitational field by planning method*；
Under the condition that the accurate gravitational field model of the target small celestial body is unknown, the landing accuracy of the lander at the preset position of the surface of the small celestial body is improved by designing a corresponding landing control strategy.
CN202010750835.4A 2020-07-30 2020-07-30 Small celestial body soft landing differential game control method in uncertain environment Active CN111846288B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010750835.4A CN111846288B (en) 2020-07-30 2020-07-30 Small celestial body soft landing differential game control method in uncertain environment

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010750835.4A CN111846288B (en) 2020-07-30 2020-07-30 Small celestial body soft landing differential game control method in uncertain environment

Publications (2)

Publication Number Publication Date
CN111846288A CN111846288A (en) 2020-10-30
CN111846288B true CN111846288B (en) 2021-09-24

Family

ID=72946265

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010750835.4A Active CN111846288B (en) 2020-07-30 2020-07-30 Small celestial body soft landing differential game control method in uncertain environment

Country Status (1)

Country Link
CN (1) CN111846288B (en)

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112631285B (en) * 2020-12-08 2021-11-23 北京理工大学 Method for quickly generating small celestial body attachment autonomous obstacle avoidance track
CN113110557B (en) * 2021-05-07 2022-02-15 北京理工大学 Minor planet landing end bounce movement guidance method
CN113221365B (en) * 2021-05-20 2023-01-10 北京理工大学 Processing method for burnup constraint in spacecraft flight game
CN114003015B (en) * 2021-10-11 2023-06-23 清华大学深圳国际研究生院 Active fault diagnosis method and device under mixed uncertainty and storage medium

Family Cites Families (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5931417A (en) * 1992-06-02 1999-08-03 Mobile Communications Holdings, Inc. Non-geostationary orbit satellite constellation for continuous coverage of northern latitudes above 25° and its extension to global coverage tailored to the distribution of populated land masses on earth
CN101608926B (en) * 2009-07-24 2012-02-01 厦门大学 Multilevel multi-modal routing navigating method
CN101692315B (en) * 2009-09-25 2011-08-10 民航总局空管局技术中心 Method for analyzing high precision 4D flight trajectory of airplane based on real-time radar data
CN102116628B (en) * 2009-12-31 2013-01-02 北京控制工程研究所 High-precision navigation method for landed or attached deep sky celestial body detector
CN101762273A (en) * 2010-02-01 2010-06-30 北京理工大学 Autonomous optical navigation method for soft landing for deep space probe
JP2020015416A (en) * 2018-07-25 2020-01-30 国立大学法人東京工業大学 Image processing device

Also Published As

Publication number Publication date
CN111846288A (en) 2020-10-30

Similar Documents

Publication Publication Date Title
CN111846288B (en) Small celestial body soft landing differential game control method in uncertain environment
CN107544067B (en) Hypersonic reentry vehicle tracking method based on Gaussian mixture approximation
CN111319802B (en) Self-adaptive curvature matching guidance method for small celestial body attachment track
CN111552003B (en) Asteroid gravitational field full-autonomous measurement system and method based on ball satellite formation
CN106227972A (en) A kind of optimization method of the steady glide trajectories of hypersonic aircraft
CN109344449B (en) Spacecraft monthly transfer orbit reverse design method
CN109270960A (en) Online Optimal Feedback reentry guidance method based on Radau puppet spectrometry
CN108153323B (en) A kind of high-altitude unmanned vehicle high-precision reentry guidance method
CN113867143B (en) Safety soft landing analysis obstacle avoidance guidance method for extraterrestrial celestial body
CN110908407B (en) Improved prediction guidance method for RLV reentry heat flow rate tracking
CN105631095A (en) Search method for multi-constrained earth-moon transfer orbit cluster with equal launch intervals
CN110309627B (en) Reachable area acquisition method for small celestial body surface bouncing movement
CN110466805B (en) Planet landing guidance method based on optimized guidance parameters
CN113467241B (en) Method for optimizing burn-up of convex curvature landing track
CN111924139A (en) Small celestial body landing obstacle avoidance constant thrust control method based on expansion early warning area
CN109799835A (en) A kind of optimal method that leaves the right or normal track of rope system towing of space junk
CN106802143A (en) A kind of hull deformation angle measuring method based on inertial instruments and Iterative-Filtering Scheme
CN110703793B (en) Method for attacking maneuvering target by adopting aircraft integral proportion guidance of attitude angle measurement
CN111361760B (en) Small celestial body surface movement track tolerance optimization method
CN110108162B (en) Remote automatic throwing drop point correction guidance control method for motion platform
CN108562293A (en) Planetary landing finite-time control method based on interference observer
CN111125874B (en) High-precision rail measurement forecasting method for movable platform
Duan et al. Trajectory tracking and online replanning for Mars entry
CN112629540B (en) Heave measurement method based on carrier attitude information
CN112904719B (en) Annular area tracking control method suitable for underwater robot position

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant