CN106778012B - A kind of small feature loss attachment detection descending trajectory optimization method - Google Patents
A kind of small feature loss attachment detection descending trajectory optimization method Download PDFInfo
- Publication number
- CN106778012B CN106778012B CN201611243319.2A CN201611243319A CN106778012B CN 106778012 B CN106778012 B CN 106778012B CN 201611243319 A CN201611243319 A CN 201611243319A CN 106778012 B CN106778012 B CN 106778012B
- Authority
- CN
- China
- Prior art keywords
- small feature
- feature loss
- optimization method
- interior
- ball
- 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
Links
Classifications
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16Z—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS, NOT OTHERWISE PROVIDED FOR
- G16Z99/00—Subject matter not provided for in other main groups of this subclass
Landscapes
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The present invention relates to a kind of small feature loss to adhere to detection descending trajectory optimization method, belongs to field of aerospace.The present invention is using the gravitational acceleration near the humorous Gravitation Field Model estimation target small feature loss of interior ball, using convex optimized algorithm solution optimal control problem.Using gravitational acceleration near the humorous Gravitation Field Model estimation small feature loss of interior ball, have the advantages that computational efficiency is high.Optimal fuel control problem is solved using convex optimized algorithm, the derivation for avoiding indirect method is complicated, and association's state variable is not easy the problem of guessing without physical significance, it is relatively simple to derive step, the calculating time is saved, it is a kind of quick, high-precision Estimation Optimization method, and acquired results meet the constraint of initial and end state, Dynamic Constraints and control constraints.
Description
Technical field
The present invention relates to a kind of small feature loss to adhere to detection descending trajectory optimization method, belongs to field of aerospace.
Background technique
Small celestial body exploration understands solar system formation and evolution, origin of life as the mankind and evolves and defend external celestial body
The important channel of shock will be one of movable main contents of the following deep space exploration, and attachment detection is people in following a period of time
The major way of class exploration small feature loss.Decline stage is the key that lander attachment small feature loss or completes to sample return detection rank
Can section play conclusive effect to safe and accurate reach the preset target area with scientific exploration value, this is under
Trajectory Design, navigation and the Guidance and control of depression of order section are proposed very high requirement.The decline process of small feature loss lander can be with
It is converted into a track optimizing problem and the tracking control problem to nominal trajectory.The nominal trajectory of setting is required to pacify
Entirely, specified landing point is accurately arrived at, meets the multiple constraints such as whole story state constraint, path constraint, control constraints, while making certain
The important performance indicator of item optimizes, such as burnup, time.Track optimizing method mainly includes based on the direct of parametric method
Method and indirect method based on Pang Te lia king minimal principle.Direct method is not necessarily to derive the transversality condition of optimization problem, avoids
The association's state initial value for solving two-point boundary value problem is sensitive difficult, thus is widely used.In addition, near for small feature loss
Track optimizing problem, it is also necessary to establish the Gravitation Field Model of gravitational acceleration near accurate description small feature loss.
In the small feature loss attachment detection descending trajectory optimization method developed, first technology [1] is (referring to Lantoine
G,Braun R.Optimal trajectories for soft landing on asteroids.Space Systems
Design Lab,Georgia Institute of Technology,Atlanta,GA,AE8900 MS Special
Problems Report, Dec.2006.) using the gravitational acceleration near polyhedral model solution target small feature loss, with energy
As optimizing index, big step-length optimization is carried out with direct method, so that estimation obtains association's state initial value of optimization problem, is then based on
Pang Te lia king principle carries out the calculating of indirect method track optimizing.Polyhedral model seeks gravitational acceleration low efficiency, and optimization algorithm is numerous
Trivial, time-consuming.
First technology [2] is (referring to Ren, Y.and Shan, J., " Reliability-Based Soft Landing
Trajectory Optimization near Asteroid with Uncertain Gravitational Field,”
Journal of Guidance, Control, and Dynamics, Vol.38, No.9,2015, pp.1810-1820.), first
The more specific energetic optimum problem of convergence region is constructed, then by adjusting homotopy coefficient, sequence is solved, finally by energetic optimum
Problem is converted into fuel optimal problem, and solution two-point boundary value problem is still needed using Homotopy, and optimization process takes a long time.
Summary of the invention
The invention aims to solve existing small feature loss attachment detection descending trajectory optimization method because drawing using polyhedron
Force field model seeks gravitational acceleration inefficient；And track optimizing resolving is carried out using indirect method, because association's state initial value is difficult to estimate
Difficult problem is solved, a kind of small feature loss attachment detection descending trajectory optimization method is provided.
A kind of small feature loss attachment detection descending trajectory optimization method, estimates target small feature loss using the humorous Gravitation Field Model of interior ball
Neighbouring gravitational acceleration, using convex optimized algorithm solution locus optimization method.
The convex optimized algorithm includes relaxation, linearisation, discretization and interior point method.
A kind of small feature loss attachment detection descending trajectory optimization method, comprising the following steps:
Step 1: by the spherical harmonic coefficient of the humorous Gravitation Field Model of ball in Least Square Method:
Brillouin's ball in small feature loss external structure, constructing interior Brillouin's ball should land with the target on small feature loss surface
Point is tangent, and centre of sphere selection should ensure that lander descending trajectory is included inside Brillouin's ball.Appoint inside interior Brillouin's ball and takes
NdataIt is a, N is calculated by polyhedral modeldataThe gravitational acceleration of a point, and 3N is constructed by the gravitational accelerationdata× 1 dimension
MatrixThe humorous gravity model spherical harmonic coefficient of interior ball is sought by least square method.
Wherein, n and m respectively indicates the order and power of Legnedre polynomial,For (a n2+ 2n) × 1 dimension
Matrix,Contain spherical harmonic coefficient in the required each rank taken
For the matrix that gravitational acceleration is constituted about the derivative of interior spherical harmonic coefficient, dimension is (n2+2n)×
3Ndata.W is a 3NdataTie up unit matrix；
Step 2: construction small feature loss attachment detection descending trajectory optimization method:
In the case where small feature loss is connected coordinate system, lander meets following kinetics equation
Wherein, r=[x, y, z]TWithThe position vector and speed of lander under respectively connected coordinate system
Vector；ω=[0,0, ω]TFor small feature loss spin angle velocity vector；T=[Tx,Ty,Tz]TFor lander thrust vectoring；meTo land
The quality of device；IspFor engine/motor specific impulse；ge=9.807 be normal gravity constant；For
Gravitational acceleration vector, is calculated by following formula:
Wherein, G is universal gravitational constant, and M is target small feature loss quality, and R is interior Brillouin's radius of a ball in step 1, δ0,m
For Kronecker delta (Ke Laoneike) function (as m=0, δ0,m=1).For interior ball required by step 1
Humorous coefficient；For the humorous Gravitation Field Model basic function of ball interior in step 1, meet following recurrence relation.
Lander meets following boundary condition
Wherein, r0, v0And m0The respectively position of original position lander, speed and quality.tfFor terminal time, rfFor
Target landing point, vfIt is constrained for terminal velocity, for soft landing problem, vf=0.
Lander thrust vectoring meets following constraint condition
0≤||T||≤Tmax (7)
Fuel optimal performance index is expressed as follows
Formula (3), (6), (7), (8) constitute descending trajectory optimization method；
Step 3: slack variable Γ is introduced into the resulting descending trajectory optimization method of step 2, to the descending trajectory
Optimization method relaxes:
It is introduced into slack variable Γ substitution descending trajectory optimization method | | T | |, then the track optimizing equation after relaxing are as follows:
Step 4: to equation linearization process obtained by step 3:
It is as follows to define new variables
The above variable is substituted into the optimization method of step 3, the optimization method linearized is
Wherein,T indicates time variable.
Step 5: carrying out sliding-model control to the resulting optimization method of step 4:
By time interval [0, tf] N parts are divided into, it obtainsThe optimization method of step 4 is carried out at discretization
Reason, after discretization, track optimizing equation is converted to parameter optimization equation, and the expression formula of parameter optimization equation is as follows:
Wherein, M=[I6,06×1], tkIndicate k-th of timing node, ukAnd σkRespectively indicate tkThe value of moment u and σ.
Step 6: being iterated solution to the parameter optimization equation in step 5 using interior point method, specific solution procedure is such as
Under:
1) enabling gravitational acceleration is a constant value ▽ V0, using the parameter optimization equation in interior point method solution procedure five, obtain
One track；
2) using the obtained track of step 1) as reference locus, calculate each node in reference locus (i.e. k=0 ...,
N the gravitational acceleration at), and bring into the parameter optimization equation in step 5, it is solved using interior point method, obtains one newly
Track, using obtained new track as the reference locus of next iteration；
3) when obtained track convergence, then optimal solution is obtained to get the optimal descending trajectory of detection is arrived.
Sliding-model control method described in step 5 uses explicit fourth order Runge-Kutta integral formula method；
Beneficial effect
A kind of small feature loss attachment detection descending trajectory optimization method given by the present invention, using the humorous Gravitation Field Model of interior ball
Estimate small feature loss gravitational acceleration nearby, has the advantages that computational efficiency is high.Optimal fuel control is solved using convex optimized algorithm
Problem, the derivation for avoiding indirect method is complicated, and association's state variable is not easy the problem of guessing without physical significance, derives step more
Simplicity has saved the calculating time, is a kind of quick, high-precision Estimation Optimization method, and acquired results meet initial and end
State constraint, Dynamic Constraints and control constraints.
Detailed description of the invention
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is simulation result schematic diagram, is most had track by four iteration altogether；Wherein (a) is the connected seat of small feature loss
Mark is the lower track of lander along the x-axis direction, is (b) track schematic diagram along the y-axis direction, is (c) track signal along the z-axis direction
Figure, is (d) the big logotype of thrust.
Specific embodiment
The invention will be further described with embodiment with reference to the accompanying drawing.
Embodiment 1
A kind of small feature loss attachment detection descending trajectory optimization method, comprising the following steps:
Step 1: by the spherical harmonic coefficient of the humorous Gravitation Field Model of ball in Least Square Method:
Brillouin's ball in small feature loss external structure, constructing interior Brillouin's ball should land with the target on small feature loss surface
Point is tangent, and centre of sphere selection should ensure that lander descending trajectory is included inside Brillouin's ball.Appoint inside interior Brillouin's ball and takes
NdataIt is a, N is calculated by polyhedral modeldataThe gravitational acceleration of a point, and 3N is constructed by the gravitational accelerationdata× 1 dimension
MatrixThe humorous gravity model spherical harmonic coefficient of interior ball is sought by least square method.
Wherein, n and m respectively indicates the order and power of Legnedre polynomial,For (a n2+ 2n) × 1 dimension
Matrix,Contain spherical harmonic coefficient in the required each rank taken
For the matrix that gravitational acceleration is constituted about the derivative of interior spherical harmonic coefficient, dimension is (n2+2n)×
3Ndata.W is a 3NdataTie up unit matrix；
Step 2: construction small feature loss attachment detection descending trajectory optimization method:
In the case where small feature loss is connected coordinate system, lander meets following kinetics equation
Wherein, r=[x, y, z]TWithThe position vector and speed of lander under respectively connected coordinate system
Vector；ω=[0,0, ω]TFor small feature loss spin angle velocity vector；T=[Tx,Ty,Tz]TFor lander thrust vectoring；meFor
The quality of land device；IspFor engine/motor specific impulse；ge=9.807 be normal gravity constant；
For gravitational acceleration vector, it is calculated by following formula:
Wherein, G is universal gravitational constant, and M is target small feature loss quality, and R is interior Brillouin's radius of a ball in step 1, δ0,m
For (Ke Laoneike) Kronecker delta function (as m=0, δ0,m=1).For interior ball required by step 1
Humorous coefficient；For the humorous Gravitation Field Model basic function of ball interior in step 1, meet following recurrence relation.
Lander meets following boundary condition
Wherein, r0, v0And m0The respectively position of original position lander, speed and quality.tfFor terminal time, rfFor
Target landing point, vfIt is constrained for terminal velocity, for soft landing problem, vf=0.
Lander thrust vectoring meets following constraint condition
0≤||T||≤Tmax (19)
Fuel optimal performance index is expressed as follows
Formula (15), (18), (19), (20) constitute descending trajectory optimization method；
Step 3: slack variable Γ is introduced into the resulting descending trajectory optimization method of step 2, to the descending trajectory
Optimization method relaxes:
It is introduced into slack variable Γ substitution descending trajectory optimization method | | T | |, then the track optimizing equation after relaxing are as follows:
Step 4: to equation linearization process obtained by step 3:
It is as follows to define new variables
The above variable is substituted into the optimization method of step 3, the optimization method linearized is
Wherein,T indicates time variable.
Step 5: carrying out sliding-model control to the resulting optimization method of step 4:
By time interval [0, tf] it is divided into N parts, it is availableBy explicit fourth order Runge-Kutta integral formula,
Discretization is carried out to the optimization method of step 4
Wherein,rk, vkAnd pkR, v and p are respectively indicated in timing node tkThe value at place, UkAnd ▽
VkState variable, control input and gravitational acceleration are respectively indicated in timing node tkThe value at place.
ukAnd σkRespectively indicate tkThe value of moment u and σ.After discretization, track optimizing equation is converted to a ginseng
Number optimization method, expression formula are as follows:
Wherein, M=[I6,06×1]。
Step 6: being iterated solution to the parameter optimization equation in step 5 using interior point method, specific solution procedure is such as
Under:
1) enabling gravitational acceleration is a constant value ▽ V0, using the parameter optimization equation in interior point method solution procedure five, obtain
One track；
2) using the obtained track of step 1) as reference locus, calculate each node in reference locus (i.e. k=0 ...,
N the gravitational acceleration at), and bring into the parameter optimization equation in step 5, it is solved using interior point method, obtains one newly
Track, using obtained new track as the reference locus of next iteration；
3) when obtained track convergence, then optimal solution is obtained to get the optimal descending trajectory of detection is arrived.
Fig. 2 is the emulation schematic diagram carried out on small feature loss 216Kleopatra.The initial position of lander be [-
150108,6010, -1034] m, target position are [- 112600,6340, -12520] m.Using small feature loss proposed by the invention
Attachment detection descending trajectory optimization method, passes through four iteration altogether, obtains final burnup optimal trajectory.As shown in Figure 2, optimize
As a result meeting every constraint condition, for lander with zero velocity soft landing in default landing point, entire calculating process is 11.4 seconds time-consuming,
Optimize obtained control force simultaneously always within the motor power upper limit of setting.
Claims (2)
1. a kind of small feature loss attachment detection descending trajectory optimization method, it is characterised in that: using the humorous Gravitation Field Model estimation of interior ball
Gravitational acceleration near target small feature loss, it is final to realize descending trajectory optimization using convex optimized algorithm solution locus optimization method；
The convex optimized algorithm includes relaxation, linearisation, discretization and interior point method；
Specific detailed step is as follows:
Step 1: by the spherical harmonic coefficient of the humorous Gravitation Field Model of ball in Least Square Method:
Brillouin's ball in small feature loss external structure, constructing interior Brillouin's ball should be with the target landing point phase on small feature loss surface
It cuts, centre of sphere selection should ensure that lander descending trajectory is included inside Brillouin's ball；Appoint inside interior Brillouin's ball and takes Ndata
It is a, N is calculated by polyhedral modeldataThe gravitational acceleration of a point, and 3N is constructed by the gravitational accelerationdata× 1 dimension matrixThe humorous Gravitation Field Model spherical harmonic coefficient of interior ball is sought by least square method；
Wherein, n and m respectively indicates the order and power of Legnedre polynomial,For (a n2+ 2n) × 1 matrix tieed up,Contain spherical harmonic coefficient in the required each rank taken
For the matrix that gravitational acceleration is constituted about the derivative of interior spherical harmonic coefficient, dimension is (n2+2n)×3Ndata；W is
One 3NdataTie up unit matrix；
Step 2: construction small feature loss attachment detection descending trajectory optimization method:
In the case where small feature loss is connected coordinate system, lander meets following kinetics equation
Wherein, r=[x, y, z]TWithThe position vector and speed arrow of lander under respectively connected coordinate system
Amount；ω=[0,0, ω]TFor small feature loss spin angle velocity vector；T=[Tx,Ty,Tz]TFor lander thrust vectoring；meTo land
The quality of device；For meTo the derivative of time；IspFor engine/motor specific impulse；ge=9.807 be normal gravity constant；For gravitational acceleration vector, it is calculated by following formula:
Wherein, G is universal gravitational constant, and M is target small feature loss quality, and R is interior Brillouin's radius of a ball in step 1, δ0,mFor
Kroneckerdelta Ke Laoneike function, as m=0, δ0,m=1；For the humorous system of interior ball required by step 1
Number；For the humorous Gravitation Field Model basic function of ball interior in step 1, meet following recurrence relation；
Lander meets following boundary condition
Wherein, r0, v0And m0The respectively position of original position lander, speed and quality；tfFor terminal time, rfFor target
Landing point, vfIt is constrained for terminal velocity, for soft landing problem, vf=0；
Lander thrust vectoring meets following constraint condition
0≤||T||≤Tmax (7)
Fuel optimal performance index is expressed as follows
Formula (3), (6), (7), (8) constitute descending trajectory optimization method；
Step 3: introducing slack variable Γ into the resulting descending trajectory optimization method of step 2, the descending trajectory is optimized
Equation relaxes:
It is introduced into slack variable Γ substitution descending trajectory optimization method | | T | |, then the track optimizing equation after relaxing are as follows:
Step 4: to equation linearization process obtained by step 3:
It is as follows to define new variables
The above variable is substituted into the optimization method of step 3, the optimization method linearized is
Wherein,T indicates time variable；
Step 5: carrying out sliding-model control to the resulting optimization method of step 4:
By time interval [0, tf] N parts are divided into, it obtainsSliding-model control, warp are carried out to the optimization method of step 4
It crosses after discretization, track optimizing equation is converted to parameter optimization equation, and the expression formula of parameter optimization equation is as follows:
Wherein, M=[I6,06×1], tkIndicate k-th of timing node, ukAnd σkRespectively indicate tkThe value of moment u and σ；
Step 6: being iterated solution to the parameter optimization equation in step 5 using interior point method, specific solution procedure is as follows:
1) enabling gravitational acceleration is a constant value ▽ V0, using the parameter optimization equation in interior point method solution procedure five, obtain a rail
Mark；
2) using the obtained track of step 1) as reference locus, each node, i.e. k=0 ..., N in reference locus, place are calculated
Gravitational acceleration, and bring into the parameter optimization equation in step 5, solved using interior point method, obtain a new rail
Mark, using obtained new track as the reference locus of next iteration；
3) when obtained track convergence, then optimal solution is obtained to get the optimal descending trajectory of detection is arrived.
2. a kind of small feature loss attachment detection descending trajectory optimization method as described in claim 1, it is characterised in that: step 5 institute
Sliding-model control method is stated using explicit fourth order Runge-Kutta integral formula method.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611243319.2A CN106778012B (en) | 2016-12-29 | 2016-12-29 | A kind of small feature loss attachment detection descending trajectory optimization method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611243319.2A CN106778012B (en) | 2016-12-29 | 2016-12-29 | A kind of small feature loss attachment detection descending trajectory optimization method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106778012A CN106778012A (en) | 2017-05-31 |
| CN106778012B true CN106778012B (en) | 2019-05-31 |
Family
ID=58923778
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201611243319.2A Active CN106778012B (en) | 2016-12-29 | 2016-12-29 | A kind of small feature loss attachment detection descending trajectory optimization method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106778012B (en) |
Families Citing this family (15)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107323692B (en) * | 2017-07-04 | 2019-10-18 | 北京理工大学 | A kind of energy optimizing method of small feature loss soft landing avoidance |
| CN107977530B (en) * | 2017-12-19 | 2021-03-09 | 南京航空航天大学 | Simplified modeling method for non-axisymmetric slender small celestial body gravitational field |
| CN108196449B (en) * | 2017-12-26 | 2020-04-24 | 北京理工大学 | Initial value determination method for covariate of optimal landing trajectory design |
| CN108516107B (en) * | 2018-02-27 | 2020-11-20 | 北京控制工程研究所 | Online engine thrust and specific impulse estimation method and system |
| CN108388135B (en) * | 2018-03-30 | 2020-11-10 | 上海交通大学 | Mars landing trajectory optimization control method based on convex optimization |
| CN108959182B (en) * | 2018-05-21 | 2021-09-17 | 北京理工大学 | Small celestial body gravitational field modeling method based on Gaussian process regression |
| US10858017B2 (en) * | 2018-07-31 | 2020-12-08 | Donglei Fan | Method of controlling vehicle to perform soft landing, and related controller and system |
| CN110309627B (en) * | 2019-08-12 | 2020-12-11 | 北京理工大学 | Reachable area acquisition method for small celestial body surface bouncing movement |
| CN110532724B (en) * | 2019-09-06 | 2021-03-26 | 北京理工大学 | Rapid online planning method for optimal path of burning consumption of small celestial body soft landing |
| CN110686683B (en) * | 2019-11-01 | 2021-03-30 | 北京理工大学 | Planetary landing trajectory online optimization method based on uneven expansion ellipsoid |
| CN110826224A (en) * | 2019-11-06 | 2020-02-21 | 北京理工大学 | Method for determining spherical harmonic coefficient of small celestial body gravitational field based on gravitational acceleration |
| CN110736470B (en) * | 2019-11-06 | 2021-04-20 | 北京理工大学 | Mixed search method for continuous thrust orbit near small celestial body in irregular shape |
| CN111552003B (en) * | 2020-05-11 | 2020-12-18 | 中国人民解放军军事科学院国防科技创新研究院 | Asteroid gravitational field full-autonomous measurement system and method based on ball satellite formation |
| CN113110559B (en) * | 2021-05-13 | 2022-03-18 | 北京理工大学 | Optimal control method for small celestial body surface bouncing movement |
| CN113777926B (en) * | 2021-09-15 | 2023-11-10 | 北京理工大学 | Optimal control method for burning up of small celestial body attached three-dimensional convex track |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102890506B (en) * | 2011-07-19 | 2015-04-15 | 北京理工大学 | Small body approaching section guidance control method based on constraint programming |
| CN105631099B (en) * | 2015-12-23 | 2019-06-28 | 北京工业大学 | A kind of small celestial body exploration device landing dynamics simulation system |
-
2016
- 2016-12-29 CN CN201611243319.2A patent/CN106778012B/en active Active
Also Published As
| Publication number | Publication date |
|---|---|
| CN106778012A (en) | 2017-05-31 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106778012B (en) | A kind of small feature loss attachment detection descending trajectory optimization method | |
| Ye et al. | State damping control: A novel simple method of rotor UAV with high performance | |
| CN106586033B (en) | The multistage linear puppet of adaptive segmentation composes broad sense mark control miss distance reentry guidance method | |
| CN113479347B (en) | Rocket vertical recovery landing zone track control method | |
| Zhao et al. | Progress in reentry trajectory planning for hypersonic vehicle | |
| CN109062241B (en) | Autonomous full-shot reentry guidance method based on linear pseudo-spectrum model predictive control | |
| Lu et al. | Real-time simulation system for UAV based on Matlab/Simulink | |
| CN110376882A (en) | Pre-determined characteristics control method based on finite time extended state observer | |
| CN103853050A (en) | PID optimization control method of four-rotor aircraft | |
| Luchtenburg et al. | Unsteady high-angle-of-attack aerodynamic models of a generic jet transport | |
| CN108196449A (en) | The covariant Determination of Initial of optimum landing path design | |
| Hua et al. | Effect of elastic deformation on flight dynamics of projectiles with large slenderness ratio | |
| CN113361013B (en) | Spacecraft attitude robust control method based on time synchronization stability | |
| CN106570285A (en) | J2 perturbation Lambert problem solving method based on state transition matrix analytic solution | |
| Yang et al. | Steady glide dynamic modeling and trajectory optimization for high lift-to-drag ratio reentry vehicle | |
| CN102566446B (en) | Method for establishing full-envelope mathematical model of unmanned helicopter based on linear model group | |
| Wan et al. | Fuel-optimal guidance for end-to-end human-mars entry, powered-descent, and landing mission | |
| Sun et al. | Altitude control for flexible wing unmanned aerial vehicle based on active disturbance rejection control and feedforward compensation | |
| CN105116905A (en) | Aircraft attitude control method | |
| CN108303874A (en) | It is a kind of for rope be the shimmy low thrust method for handover control of space Tugboat system | |
| Thangam et al. | Application of a new K-tau model to near wall turbulent flows | |
| Ming et al. | Velocity Control Based on Active Disturbance Rejection for Air‐Breathing Supersonic Vehicles | |
| Barton et al. | New methodologies for onboard generation of TAEM trajectories for autonomous RLVs | |
| CN110321598A (en) | A kind of Spacecraft Relative Motion Analytical Solution method under J2 perturbation conditions | |
| CN104657595B (en) | A kind of individual particle drag force model coefficient scaling method |
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 |