CN107621829A - A kind of place of safety expansion method of guidance of planetary landing obstacle avoidance - Google Patents

A kind of place of safety expansion method of guidance of planetary landing obstacle avoidance Download PDF

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CN107621829A
CN107621829A CN201710844211.7A CN201710844211A CN107621829A CN 107621829 A CN107621829 A CN 107621829A CN 201710844211 A CN201710844211 A CN 201710844211A CN 107621829 A CN107621829 A CN 107621829A
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detector
obstacle
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CN107621829B (en
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崔平远
袁旭
朱圣英
高艾
徐瑞
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Beijing Institute of Technology BIT
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Abstract

A kind of place of safety expansion method of guidance of planetary landing obstacle avoidance disclosed by the invention, belongs to deep-space detection field.The present invention defines landing solid point connection coordinate system and error ellipsoid main shaft coordinate system first；Landing kinetics equation is established in the case where landing point connects firmly coordinate system；Ellipsoid inflatable air area, safe distance desired value of the calculating detector with respect to obstacle are determined according to detector position error n σ ellipsoids；Liapunov function is built with respect to the safe distance desired value of obstacle based on detector's status and detector, obstacle avoidance Guidance Law is designed using Liapunov stability principle, utilize acceleration instruction a control detector landing paths, reduce the influence that planetary surface disturbs more, uncertain environment guides to detector obstacle avoidance, planetary surface obstacle is effectively evaded, realizes discretionary security precision landing.It is analytical form that what the present invention asked for, which controls acceleration instruction, without complex calculations such as integrations, meets online feedback realtime control requirement, is advantageous to engineer applied.

Description

A kind of place of safety expansion method of guidance of planetary landing obstacle avoidance
Technical field
The present invention relates to a kind of planetary landing obstacle avoidance method of guidance, more particularly to a kind of planetary landing obstacle avoidance Place of safety expands method of guidance, belongs to deep-space detection field.
Background technology
Planetary landing obstacle avoidance problem be planetary landing detection major issue, relation planetary landing detection mission into Lose the safety with detector.Because the precision and sensor operating distance of in-orbit mapping are limited, crater existing for planetary surface, Rock, slope, massif etc. are difficult to carry out in the stage of being diversion completely and accurate mapping is, it is necessary to these threats in landing mission The obstacle for safety of landing carries out detection in real time with evading.To obtain more science return, following planetary landing task will seek Landed in the complex topographic territory of more scientific value, therefore detector must possess online obstacle detection and dodging ability, to protect Hinder detector safety, realize that discretionary security lands.
First technology [1] is (referring to Lopez, Ismael, McInnes, Colin R.Autonomous rendezvous using artificial potential function guidance[J].Journal of Guidance,Control, and Dynamics,1995,18(2):237-241.), for Autonomous rendezvous and docking problem, it is proposed that a kind of artificial potential function system Control method is led, while realizing autonomous rendezvous, many places obstacle can be evaded.First technology [2] is (referring to Zhu S Y,Cui P Y,Hu H J,Hazard detection and avoidance for planetary landing based on Lyapunov control method[C].Intelligent Control and Automation.Beijing: [s.n.], 2012), small feature loss landing obstacle avoidance problem have studied using potential function method of guidance, current according to detector Potential energy chooses Artificial potential functions with threat of the obstacle terrain to detector, and is derived and made by Liapunov stability principle Lead rule, it is thus possible to ensure to evade the obstacle during landing while detector reaches target landing point.
The interference of planetary landing dynamics environment is more, and non-linear and uncertainty is strong, to detector landing and obstacle avoidance system Lead and bring very big challenge with control.When detector's status is present it is larger uncertain when, tradition side that the first technology of the above represents Method possibly can not effectively assess the threat degree of obstacle opposing detector virtual condition, so as to cause obstacle avoidance to fail.
The content of the invention
A kind of place of safety expansion method of guidance of planetary landing obstacle avoidance disclosed by the invention, technical problems to be solved It is to reduce the influence that planetary landing disturbs more, uncertain environment guides to detector obstacle avoidance, planetary surface obstacle is carried out Effectively evade, realize discretionary security precision landing.
The purpose of the present invention is realized by the following method.
A kind of place of safety expansion method of guidance of planetary landing obstacle avoidance disclosed by the invention, defines landing solid point first Join coordinate system and error ellipsoid main shaft coordinate system.Landing kinetics equation is established in the case where landing point connects firmly coordinate system.According to detection Device site error n σ ellipsoids determine the ellipsoid inflatable air area of detector, and then calculating detector refers to respect to the safe distance of obstacle Scale value.Liapunov function is built with respect to the safe distance desired value of obstacle based on detector's status and detector, utilizes Lee Ya Punuofu stability principles design obstacle avoidance Guidance Law, using acceleration instruction a control detector landing paths, reduce row The influence that star catalogue face disturbs more, uncertain environment guides to detector obstacle avoidance, is effectively evaded to planetary surface obstacle, Realize discretionary security precision landing.
A kind of place of safety expansion method of guidance of planetary landing obstacle avoidance disclosed by the invention, comprises the following steps：
Step 1: define landing solid point connection coordinate system and error ellipsoid main shaft coordinate system.
Define landing solid point connection coordinate system (x, y, z)：Origin of coordinates O is target landing point, and z-axis is along from small feature loss barycenter Oc To origin O line directionY-axis is located in the plane that z-axis forms with small feature loss spin main shaft and perpendicular to z-axis, x-axis (x, y, z) coordinate system is set to meet right-hand rule.
Define error ellipsoid main shaft coordinate system (xE,yE,zE)：Origin of coordinates OEAt detector position estimate, xE, yE,zEThree main shafts of the axle respectively with detector position error n σ ellipsoids overlap, and meet right-hand rule.
Step 2: establish landing kinetics equation in the case where landing point connects firmly coordinate system.
When target celestial body is small feature loss, landing kinetics equation of the detector in the case where landing point connects firmly coordinate system is：
Wherein r=[x, y, z]TFor position vector of the detector in the case where landing point connects firmly coordinate system, v=[vx,vy,vz]TFor The velocity of detector, ω=[ωx,ωy,ωz]TFor target celestial body spin angle velocity vector, g=[gx,gy,gz]TFor detection The target celestial body gravitational acceleration that device is subject to, a are the control acceleration instruction applied.
When target celestial body is planet, spin angle velocity ω can be neglected, detector in the case where landing point connects firmly coordinate system Land kinetics equation is：
Step 3: determine the ellipsoid inflatable air area of detector.
According to detector's status estimated information calculating detector site error n σ ellipsoids, by site error n σ ellipsoidal surfaces and Internal part is set to the ellipsoid inflatable air area of detector.The position estimation error of detector meets the Gauss point that average is zero Cloth, in the case where landing point connects firmly coordinate system, physical location r estimate i.e. average isThe site error covariance matrix of detector For C.
Eigenvalues Decomposition is carried out to detector position error co-variance matrix C：
UTCU=D (3)
Diagonal matrix D diagonal entry be detector position error co-variance matrix C each characteristic value, matrix U it is each It is classified as the characteristic vector of corresponding each characteristic value.Orthogonal transfer matrix UTFor from define detector position error co-variance matrix Land point connects firmly coordinate system (x, y, z) and arrives error ellipsoid main shaft coordinate system (xE,yE,zE) transition matrix.Detector is in error ellipsoid Position in main shaft coordinate system is：
OrderThen detector position error n σ ellipsoid equations are：
rE TErE=1 (5)
Detector ellipsoid inflatable air area is the portion of the detector position error n σ ellipsoidal surfaces and inside shown in formula (5) Point, expression formula is：
rE TErE≤1 (6)
Step 4: safety of the ellipsoid inflatable air area calculating detector of the detector determined according to step 3 with respect to obstacle Range index value.
Detector considers the influence factor of obstacle avoidance track, described barrier with respect to the safe distance desired value of obstacle The influence factor for evading track is hindered to include detector's status uncertain factor and control constraints factor.Calculating detector first The minimum range of ellipsoid inflatable air offset obstacle, then the control safe distance value of setting is subtracted, obtain safe distance desired value D。
The minimum range of calculating detector ellipsoid inflatable air offset obstacle first, i.e. detector position error n σ ellipsoids away from The minimum range of obstacle.
Consider obstacle location and size, obstacle is modeled as hemispherical, obstacle center is connected firmly under coordinate system i.e. with landing point Hemisphere sphere centre coordinate rc, and obstacle reference radius is position and the size that half radius of a ball R describes obstacle.Obstacle center is ellipse in error Coordinate under ball spindle coordinate system is：
According to obstacle center and the position relationship of detector position error n σ ellipsoids, selection performs step 4.1 or step 4.2, obtain minimum range d of the detector position error n σ ellipsoids away from obstaclee。
Step 4.1, it is centrally located at outside detector position error n σ ellipsoids when obstacle, i.e.,：
rcE TErcE＞ 1 (8) sets the point r on detector position error n σ ellipsoidal surfacessIt is ellipsoidal surfaces away from obstacle center rc The minimum point of distance.Under error ellipsoid main shaft coordinate system, point rsCoordinate be：
And meet below equation：
rsE=(I+ λ E)-1rcE (10)
rcE T(I+λE)-TE(I+λE)-1rcE- 1=0 (11)
λ is Lagrange multiplier in formula.Solve equation (10)-(11) and obtain λ value, so as to obtain coordinate rsE.Because of rcEIt is located at Outside detector position error n σ ellipsoids, therefore have uniquely away from r on ellipsoidcENearest point, corresponding λ are uniquely more than zero solution.
Detector position error n σ ellipsoids are away from obstacle center rcMinimum range be：
dc=| | rsE-rcE| |=| | rs-rc|| (12)
Wherein
Work as dc＞ R, represent that obstacle is integrally located at outside detector position error n σ ellipsoids, detector position error n σ ellipsoids Minimum range away from obstacle is：
de=dc-R (13)
Work as dc≤ R, represent that detector position error n σ ellipsoids intersect with obstacle, obstacle part is located at detector position error Inside n σ ellipsoids, minimum range d of the detector position error n σ ellipsoids away from obstacleeFor 0.
Inside detector position error n σ ellipsoids or on surface, i.e., if step 4.2, obstacle are centrally located at：
rcE TErcE≤ 1 (14) then detector position error n σ ellipsoids away from obstacle center rcMinimum range be 0.Accordingly Ground, obstacle in whole or in part inside the detector position error n σ ellipsoids, detector position error n σ ellipsoids away from obstacle most Small distance deFor 0.
Minimum range d of the detector position error n σ ellipsoids away from obstacle obtained with described step 4.1 or step 4.2e Subtract control safe distance ds, obtain safe distance desired value D of the detector with respect to obstacle：
D=de-ds,de≥ds (15)
Wherein control safe distance dsConsider the thrust spoke including detector thruster configuration and each axial thrust device Control ability constraint including value, control accuracy, value is preset according to detector configuring condition, to reflect detector control Influence of the capacity consistency to detector obstacle avoidance maneuverability.
When minimum range of the detector position error n σ ellipsoids away from obstacle is less than control safe distance, safe distance index Value D is 0, i.e.,：
D=0, de＜ ds (16)
When detector is 0 with respect to the safe distance desired value of obstacle, represent state is uncertain and control constraints Under the influence of, detector may collide with obstacle, and the security of detector now is relatively low.
Step 5: the safe distance desired value obtained according to step 4 builds liapunov function.
In the case where landing point connects firmly coordinate system, the potential field function phi on detector's status is builtq
φq=xTQx (17)
Wherein x=[x, y, z, vx,vy,vz]TFor detector's status variable, Q is with qi＞ 0, i=1 ..., 6 be diagonal Diagonal matrix.The potential field that above formula represents, the minimum point of existence anduniquess, is detector dbjective state x=0.As long as ensure to visit The direction that surveying device state x reduces along potential field is advanced, and detector's status automatic will level off to target landing state, i.e., while meet mesh Mark landing position and speed.
According to safe distance desired value D of the detector obtained in step 4 with respect to obstacle, build what is threatened on obstacle Potential field function phih
Wherein, DiSafe distance desired value of the detector with respect to i-th of obstacle is represented, k represents the quantity of obstacle, the Hes of ψ ＞ 0 σ ＞ 0 are parameter.As safe distance desired value D of the detector with respect to obstacleiDuring reduction, potential field function phihValue increase.If design The direction that Guidance Law makes detector and reduced along potential field is advanced, and detector will realize obstacle avoidance automatically.
Finally, the liapunov function φ of following form is built：
Liapunov function is by φqAnd φhTwo parts form so that detector dbjective state is unique complete in potential field Office minimum point, and when detector is close to obstacle potential field value increase, as long as therefore design control acceleration instruction a make detector Direction is reduced along potential field to advance, you can while realize autonomous obstacle avoidance and autonomous accurate soft landing.
Step 6: design obstacle avoidance Guidance Law obtains the control acceleration a described in step 5, to realize autonomous obstacle Evade and autonomous accurate soft landing.
The value of safe distance index D in step 4, selection perform step 6.1 or step 6.2, obtain corresponding Control acceleration instruction a.
Step 6.1, it is all higher than 0 when the safe distance desired value of relatively each obstacle of detector, i.e.,：
Di＞ 0, i=1 ..., k (20)
Order
A=aq+ah (23)
Wherein, κ is arithmetic number.And when target celestial body is small feature loss：
Be kinetics equation (1) formula with x, y, the item relevant with spin angle velocity ω after the expansion of z-axis component form.Work as target When celestial body is planet, ξx=ξy=ξz=0.
Step 6.2, when detector with respect to certain obstacle safe distance desired value be 0, that is, exist：
DjThe security of=0,1≤j≤k (25) now detectors is relatively low.To ensure detector safety, start " urgent State ", detector is set promptly to increase, it is corresponding control acceleration to instruct to be：
A=[0,0, amax]T (26)
Wherein amaxFor the thruster peak acceleration of z-axis positive direction.
The acceleration instruction a control detector landing paths asked for using step 6, are reduced planetary surface and disturb more, be not true Know the influence that environment guides to detector obstacle avoidance, planetary surface obstacle is effectively evaded, realize that discretionary security is accurate Land.
It is analytical form that what step 6 was asked for, which controls acceleration instruction a, without complex calculations such as integrations, meets online feedback The requirement of real-time of control.
N values are depending on ellipsoid inflatable air area size requirement in described detector position error n σ ellipsoids, preferably n Value is 3.
Beneficial effect：
1st, the place of safety expansion method of guidance of a kind of planetary landing obstacle avoidance disclosed by the invention, by introducing detector Ellipsoid inflatable air area and corresponding safe distance index, and control constraints uncertain to detector position etc. to landing rail The influence of mark safety is quantitatively described, and obstacle avoidance Guidance Law is generated based on dynamic safe distance index, can be to planet The obstacle on surface is effectively evaded, and realizes discretionary security precision landing, and adapt to planetary landing interference it is more, it is uncertain by force Dynamics environment condition.Under conditions of detector position has larger uncertainty, obstacle avoidance significant effect is better than tradition Obstacle avoidance method.
2nd, the place of safety expansion method of guidance of a kind of planetary landing obstacle avoidance disclosed by the invention, by building Li Yapu Promise husband's function, obstacle avoidance Guidance Law is designed using Liapunov stability, guarantee system is Existence of Global Stable.In addition, when spy When to survey device with respect to the safe distance desired value of certain obstacle be zero, by detector is promptly increased with avoid may generation touch Hit, further ensure detector safety.
3rd, a kind of place of safety expansion method of guidance of planetary landing obstacle avoidance disclosed by the invention, the control asked for accelerate Degree instruction is analytical form, without complex calculations such as integrations, meets the requirement of real-time of online feedback control, being advantageous to engineering should With.
Brief description of the drawings
Fig. 1 is the flow chart of the inventive method；
Fig. 2 is that landing point connects firmly coordinate system schematic diagram；
Fig. 3 is error ellipsoid main shaft coordinate system schematic diagram；
Fig. 4 is the shaft position simulation curve of the inventive method three；
Fig. 5 is the axle speed simulation curve of the inventive method three；
Fig. 6 is the inventive method 3-axis acceleration command simulation curve；
Fig. 7 is the inventive method three-dimensional landing simulation track；
Fig. 8 is that the minimum range at Monte Carlo simulation middle-range obstacle center is distributed (obstacle 1, conventional method)；
Fig. 9 is that the minimum range at Monte Carlo simulation middle-range obstacle center is distributed (obstacle 2, conventional method)；
Figure 10 is that the minimum range at Monte Carlo simulation middle-range obstacle center is distributed (obstacle 1, the inventive method)；
Figure 11 is that the minimum range at Monte Carlo simulation middle-range obstacle center is distributed (obstacle 2, the inventive method).
Embodiment
The invention will be further described with embodiment below in conjunction with the accompanying drawings.
Embodiment 1
A kind of place of safety expansion method of guidance of planetary landing obstacle avoidance, it is real by taking small feature loss landing obstacle avoidance as an example Existing present embodiment method comprises the following steps, as shown in Figure 1：
Step 1: define landing solid point connection coordinate system and error ellipsoid main shaft coordinate system.
Define landing solid point connection coordinate system (x, y, z)：Origin of coordinates O is target landing point, and z-axis is along from small feature loss barycenter Oc To origin O line directionY-axis is located in the plane that z-axis forms with small feature loss spin main shaft and perpendicular to z-axis, x-axis (x, y, z) coordinate system is set to meet right-hand rule.
Define error ellipsoid main shaft coordinate system (xE,yE,zE)：Origin of coordinates OEAt detector position estimate, xE, yE,zEThree main shafts of the axle respectively with detector position error n σ ellipsoids overlap, and meet right-hand rule.
Step 2: establish landing kinetics equation in the case where landing point connects firmly coordinate system.
When target celestial body is small feature loss, landing kinetics equation of the detector in the case where landing point connects firmly coordinate system is：
Wherein r=[x, y, z]TFor position vector of the detector in the case where landing point connects firmly coordinate system, v=[vx,vy,vz]TFor The velocity of detector, ω=[ωx,ωy,ωz]TFor target celestial body spin angle velocity vector, g=[gx,gy,gz]TFor detection The target celestial body gravitational acceleration that device is subject to, a are the control acceleration instruction applied.
When target celestial body is planet, spin angle velocity ω can be neglected, detector in the case where landing point connects firmly coordinate system Land kinetics equation is：
Step 3: determine the ellipsoid inflatable air area of detector.
According to detector's status estimated information calculating detector site error n σ ellipsoids, by site error n σ ellipsoidal surfaces and Internal part is set to the ellipsoid inflatable air area of detector.The position estimation error of detector meets the Gauss point that average is zero Cloth, in the case where landing point connects firmly coordinate system, physical location r estimate i.e. average isThe site error covariance matrix of detector For C.
Eigenvalues Decomposition is carried out to detector position error co-variance matrix C：
UTCU=D
Diagonal matrix D diagonal entry be detector position error co-variance matrix C each characteristic value, matrix U it is each It is classified as the characteristic vector of corresponding each characteristic value.Orthogonal transfer matrix UTFor from define detector position error co-variance matrix Land point connects firmly coordinate system (x, y, z) and arrives error ellipsoid main shaft coordinate system (xE,yE,zE) transition matrix.Detector is in error ellipsoid Position in main shaft coordinate system is：
In error ellipsoid main shaft coordinate system, the equiprobability density face of detector position error distribution, i.e. n σ error ellipsoids Equation is：
rE TD-1rE=n2 (27)
OrderThen detector position error n σ ellipsoid equations are：
rE TErE=1
Detector ellipsoid inflatable air area is the portion of the detector position error n σ ellipsoidal surfaces and inside shown in formula (5) Point, expression formula is：
rE TErE≤1
Step 4: safety of the ellipsoid inflatable air area calculating detector of the detector determined according to step 3 with respect to obstacle Range index value.
Detector considers the influence factor of obstacle avoidance track, described barrier with respect to the safe distance desired value of obstacle The influence factor for evading track is hindered to include detector's status uncertain factor and control constraints factor.Calculating detector first The minimum range of ellipsoid inflatable air offset obstacle, then the control safe distance value of setting is subtracted, obtain safe distance desired value D。
The minimum range of calculating detector ellipsoid inflatable air offset obstacle first, i.e. detector position error n σ ellipsoids away from The minimum range of obstacle.
Consider obstacle location and size, obstacle is modeled as hemispherical, obstacle center is connected firmly under coordinate system i.e. with landing point Hemisphere sphere centre coordinate rc, and obstacle reference radius is position and the size that half radius of a ball R describes obstacle.Obstacle center is ellipse in error Coordinate under ball spindle coordinate system is：
According to obstacle center and the position relationship of detector position error n σ ellipsoids, selection performs step 4.1 or step 4.2, obtain minimum range d of the detector position error n σ ellipsoids away from obstaclee。
Step 4.1, it is centrally located at outside detector position error n σ ellipsoids when obstacle, i.e.,：
rcE TErcE＞ 1
If the point r on detector position error n σ ellipsoidal surfacessIt is ellipsoidal surfaces away from obstacle center rcThe minimum point of distance. Under error ellipsoid main shaft coordinate system, point rsCoordinate be：
And meet below equation：
rsE=(I+ λ E)-1rcE
rcE T(I+λE)-TE(I+λE)-1rcE- 1=0
λ is Lagrange multiplier in formula.Solve equation (10)-(11) and obtain λ value, so as to obtain coordinate rsE.Because of rcEIt is located at Outside detector position error n σ ellipsoids, therefore have uniquely away from r on ellipsoidcENearest point, corresponding λ are uniquely more than zero solution.
Detector position error n σ ellipsoids are away from obstacle center rcMinimum range be：
dc=| | rsE-rcE| |=| | rs-rc‖
Wherein
Work as dc＞ R, represent that obstacle is integrally located at outside detector position error n σ ellipsoids, detector position error n σ ellipsoids Minimum range away from obstacle is：
de=dc-R
Work as dc≤ R, represent that detector position error n σ ellipsoids intersect with obstacle, obstacle part is located at detector position error Inside n σ ellipsoids, minimum range d of the detector position error n σ ellipsoids away from obstacleeFor 0.
Inside detector position error n σ ellipsoids or on surface, i.e., if step 4.2, obstacle are centrally located at
rcE TErcE≤1
Then detector position error n σ ellipsoids are away from obstacle center rcMinimum range be 0.Correspondingly, obstacle is in whole or in part Inside detector position error n σ ellipsoids, minimum range d of the detector position error n σ ellipsoids away from obstacleeFor 0.
Minimum range d of the detector position error n σ ellipsoids away from obstacle obtained with described step 4.1 or step 4.2e Subtract control safe distance ds, obtain safe distance desired value D of the detector with respect to obstacle：
D=de-ds,de≥ds
Wherein control safe distance dsConsider the thrust spoke including detector thruster configuration and each axial thrust device Control ability constraint including value, control accuracy, value is preset according to detector configuring condition, to reflect detector control Influence of the capacity consistency to detector obstacle avoidance maneuverability.
When minimum range of the detector position error n σ ellipsoids away from obstacle is less than control safe distance, safe distance index Value D is 0, i.e.,：
D=0, de＜ ds
When detector is 0 with respect to the safe distance desired value of obstacle, represent state is uncertain and control constraints Under the influence of, detector may collide with obstacle, and the security of detector now is relatively low.
Step 5: the safe distance desired value obtained according to step 4 builds liapunov function.
In the case where landing point connects firmly coordinate system, the potential field function phi on detector's status is builtq
φq=xTQx
Wherein x=[x, y, z, vx,vy,vz]TFor detector's status variable, Q is with qi＞ 0, i=1 ..., 6 be diagonal Diagonal matrix.The potential field that above formula represents, the minimum point of existence anduniquess, is detector dbjective state x=0.As long as ensure to visit The direction that surveying device state x reduces along potential field is advanced, and detector's status automatic will level off to target landing state, i.e., while meet mesh Mark landing position and speed.
According to safe distance desired value D of the detector obtained in step 4 with respect to obstacle, build what is threatened on obstacle Potential field function phih
Wherein, DiSafe distance desired value of the detector with respect to i-th of obstacle is represented, k represents the quantity of obstacle, the Hes of ψ ＞ 0 σ ＞ 0 are parameter.As safe distance desired value D of the detector with respect to obstacleiDuring reduction, potential field function phihValue increase.If design The direction that Guidance Law makes detector and reduced along potential field is advanced, and detector will realize obstacle avoidance automatically.
Finally, the liapunov function φ of following form is built：
Liapunov function is by φqAnd φhTwo parts form so that detector dbjective state is unique complete in potential field Office minimum point, and when detector is close to obstacle potential field value increase, as long as therefore design control acceleration instruction a make detector Direction is reduced along potential field to advance, you can while realize autonomous obstacle avoidance and autonomous accurate soft landing.
Because Q is positive definite matrix, thus：
And φh＞ 0, then to any x ≠ 0, have：
φ ＞ 0 (29)
And
φ → ∞, when | | x | | → ∞ (30)
Step 6: design obstacle avoidance Guidance Law obtains the control acceleration a described in step 5, to realize autonomous obstacle Evade and autonomous accurate soft landing.
The value of safe distance index D in step 4, selection perform step 6.1 or step 6.2, obtain corresponding Control acceleration instruction a.
Step 6.1, it is all higher than 0 when the safe distance desired value of relatively each obstacle of detector, i.e.,：
Di＞ 0, i=1 ..., k
According to Lyapunov stability theory, to make system stable, in addition to the condition for meeting formula (28)-(30), also need Meet：
I.e.：
Wherein,
Due to
Wherein Δ r is random error.And rsOn detector position error n σ ellipsoids, i.e.,
Wherein Δ rsIt is unrelated with r.Thus：
rs=r- Δ r+ Δs rs (37)
Then
Order
A=aq+ah
Wherein, κ is arithmetic number.And when target celestial body is small feature loss：
Be kinetics equation (1) formula with x, y, the item relevant with spin angle velocity ω after the expansion of z-axis component form.Work as target When celestial body is planet, ξx=ξy=ξz=0.
During the instruction a of control acceleration more than applying to detector, meet
Condition (31) is also set up, and system is Existence of Global Stable.
Step 6.2, when detector with respect to certain obstacle safe distance desired value be 0, that is, exist
Dj=0,1≤j≤k
Now the security of detector is relatively low.For ensure detector safety, start " state of emergency ", make detector it is urgent on Rise, it is corresponding control acceleration to instruct to be：
A=[0,0, amax]T
Wherein amaxFor the thruster peak acceleration of z-axis positive direction.
The acceleration instruction a control detector landing paths asked for using step 6, are reduced planetary surface and disturb more, be not true Know the influence that environment guides to detector obstacle avoidance, planetary surface obstacle is effectively evaded, realize that discretionary security is accurate Land.
It is analytical form that what step 6 was asked for, which controls acceleration instruction a, without complex calculations such as integrations, meets online feedback The requirement of real-time of control.
N values are depending on ellipsoid inflatable air area size requirement in described detector position error n σ ellipsoids, preferably n Value is 3.
Embodiment 1 carries out simulating, verifying by target satellite of 433Eros asteroids, and simulated conditions are：Seat is connected firmly in landing point Under mark system, the initial position of detector is [1300, -1400,200]TM, initial velocity are [- 1,0,0]TM/s, target location are Landing point connects firmly coordinate origin, target velocity zero；Small feature loss surface interruptions center is respectively [500, -600]TM (barriers 1) and [340, -360] hinderTM (obstacle 2), obstacle reference radius are 80m；Maximum of the detector in each axial lifting force device Thrust acceleration is 0.05m/s2, it is 1m to control safe distance.
In the case where landing point connects firmly coordinate system, the shaft position estimation error criterion difference of detector three is 10m, and simulation time is 3500s, the position of the axle of detector landing mission three, speed, acceleration instruct curve difference as Figure 4-Figure 6, detector three It is as shown in Figure 5 to tie up landing path.Fig. 4, Fig. 5 show that the shaft position of detector three, speed converge on zero, and detector is realized accurate Soft landing；In Fig. 6, region that the instruction of control acceleration that Guidance Law provides changes greatly corresponds to be passed through in detector landing mission Two barrier zones；Fig. 7 shows that detector is successfully evaded in landing mission to two obstacles, and lands in mesh Mark landing point.Simulation result shows, the place of safety expansion method of guidance of planetary landing obstacle avoidance proposed by the present invention can be Obstacle avoidance and accurate soft landing are independently realized in the case of detector position evaluated error being present.
Further carrying out Monte Carlo simulation verifies the inventive method in the case of detector position evaluated error is larger Obstacle avoidance effect, and compared with traditional potential function method of guidance.The shaft position estimation error criterion difference of detector three is 60m, other simulated conditions are constant, carry out 500 emulation.
In Monte Carlo simulation, with detector in landing mission enter certain obstacle reference radius within be and the obstacle The standard to collide, then the reference radius in whole obstacles (is detector in this emulation all the time in landing mission It is obstacle avoidance success beyond 80m).Monte Carlo simulation result shows the feelings of larger evaluated error be present in detector position Under condition, traditional potential function method of guidance is 83.1% (Fig. 8) to the success rate of evading of obstacle 1, and the success rate of evading to obstacle 2 is 67.2% (Fig. 9), corresponding landing mission obstacle avoidance entirety success rate are 59.2%；The inventive method is to obstacle 1 and obstacle 2 Success rate of evading be 100% (Figure 10, Figure 11), corresponding landing mission obstacle avoidance entirety success rate is 100%.Due to The uncertainty of detector position information is considered in the derivation of Guidance Law and by detector ellipsoid inflatable air area and Corresponding safe distance index quantification description, the inventive method have more preferable obstacle avoidance performance under condition of uncertainty, especially Its detector position uncertainty is larger, under more obstacle MODEL OVER COMPLEX TOPOGRAPHYs, obstacle avoidance success rate is significantly higher than traditional gesture Function method of guidance.
Above-described specific descriptions, the purpose, technical scheme and beneficial effect of invention are carried out further specifically It is bright, the specific embodiment that the foregoing is only the present invention is should be understood that, for explaining the present invention, is not used to limit this The protection domain of invention, within the spirit and principles of the invention, any modification, equivalent substitution and improvements done etc. all should Within protection scope of the present invention.

Claims (7)

  1. A kind of 1. place of safety expansion method of guidance of planetary landing obstacle avoidance, it is characterised in that：Comprise the following steps,
    Step 1: define landing solid point connection coordinate system and error ellipsoid main shaft coordinate system；
    Define landing solid point connection coordinate system (x, y, z)：Origin of coordinates O is target landing point, and z-axis is along from small feature loss barycenter OcTo original Point O line directionY-axis is located at z-axis with making in the plane of small feature loss spin main shaft composition and perpendicular to z-axis, x-axis (x, y, z) coordinate system meets right-hand rule；
    Define error ellipsoid main shaft coordinate system (xE,yE,zE)：Origin of coordinates OEAt detector position estimate, xE,yE,zEAxle Three main shafts with detector position error n σ ellipsoids overlap respectively, and meet right-hand rule；
    Step 2: establish landing kinetics equation in the case where landing point connects firmly coordinate system；
    When target celestial body is small feature loss, landing kinetics equation of the detector in the case where landing point connects firmly coordinate system is：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>r</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>v</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>v</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>g</mi> <mo>-</mo> <mn>2</mn> <mi>&amp;omega;</mi> <mo>&amp;times;</mo> <mi>v</mi> <mo>-</mo> <mi>&amp;omega;</mi> <mo>&amp;times;</mo> <mi>&amp;omega;</mi> <mo>&amp;times;</mo> <mi>r</mi> <mo>+</mo> <mi>a</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    Wherein r=[x, y, z]TFor position vector of the detector in the case where landing point connects firmly coordinate system, v=[vx,vy,vz]TFor detection The velocity of device, ω=[ωx,ωy,ωz]TFor target celestial body spin angle velocity vector, g=[gx,gy,gz]TFor detector by The target celestial body gravitational acceleration arrived, a are the control acceleration instruction applied；
    When target celestial body is planet, spin angle velocity ω be can be neglected, and landing of the detector in the case where landing point connects firmly coordinate system is moved Mechanical equation is：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>r</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>v</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>v</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>g</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    Step 3: determine the ellipsoid inflatable air area of detector；
    According to detector's status estimated information calculating detector site error n σ ellipsoids, by site error n σ ellipsoidal surfaces and inside Part be set to the ellipsoid inflatable air area of detector；The position estimation error of detector meets the Gaussian Profile that average is zero, In the case where landing point connects firmly coordinate system, physical location r estimate i.e. average isThe site error covariance matrix of detector is C；
    Eigenvalues Decomposition is carried out to detector position error co-variance matrix C：
    UTCU=D (3)
    Diagonal matrix D diagonal entry is detector position error co-variance matrix C each characteristic value, and matrix U is respectively classified as The characteristic vector of corresponding each characteristic value；Orthogonal transfer matrix UTFor from define detector position error co-variance matrix landing point Connect firmly coordinate system (x, y, z) and arrive error ellipsoid main shaft coordinate system (xE,yE,zE) transition matrix；Detector is in error ellipsoid main shaft Position in coordinate system is：
    <mrow> <msub> <mi>r</mi> <mi>E</mi> </msub> <mo>=</mo> <msup> <mi>U</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <mover> <mi>r</mi> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    OrderThen detector position error n σ ellipsoid equations are：
    rE TErE=1 (5)
    Detector ellipsoid inflatable air area be formula (5) shown in detector position error n σ ellipsoidal surfaces and inside part, table It is up to formula：
    rE TErE≤1 (6)
    Step 4: safe distance of the ellipsoid inflatable air area calculating detector of the detector determined according to step 3 with respect to obstacle Desired value；
    Detector considers the influence factor of obstacle avoidance track with respect to the safe distance desired value of obstacle；Detection is calculated first The minimum range of the ellipsoid inflatable air offset obstacle of device, then the control safe distance value of setting is subtracted, obtain safe distance and refer to Scale value D；
    The minimum range of calculating detector ellipsoid inflatable air offset obstacle first, i.e. detector position error n σ ellipsoids are away from obstacle Minimum range；
    Consider obstacle location and size, obstacle is modeled as hemispherical, obstacle center i.e. hemisphere under coordinate system is connected firmly with landing point Sphere centre coordinate rc, and obstacle reference radius is position and the size that half radius of a ball R describes obstacle；Obstacle center is in error ellipsoid master Coordinate under axis coordinate system is：
    <mrow> <msub> <mi>r</mi> <mrow> <mi>c</mi> <mi>E</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>U</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <mo>-</mo> <mover> <mi>r</mi> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    According to obstacle center and the position relationship of detector position error n σ ellipsoids, selection performs step 4.1 or step 4.2, obtained To minimum range d of the detector position error n σ ellipsoids away from obstaclee；
    Step 4.1, it is centrally located at outside detector position error n σ ellipsoids when obstacle, i.e.,：
    rcE TErcE＞ 1 (8)
    If the point r on detector position error n σ ellipsoidal surfacessIt is ellipsoidal surfaces away from obstacle center rcThe minimum point of distance；By mistake Under poor ellipsoid main shaft coordinate system, point rsCoordinate be：
    <mrow> <msub> <mi>r</mi> <mrow> <mi>s</mi> <mi>E</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>U</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mi>s</mi> </msub> <mo>-</mo> <mover> <mi>r</mi> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    And meet below equation：
    rsE=(I+ λ E)-1rcE (10)
    rcE T(I+λE)-TE(I+λE)-1rcE- 1=0 (11)
    λ is Lagrange multiplier in formula；Solve equation (10)-(11) and obtain λ value, so as to obtain coordinate rsE；Because of rcEPositioned at detection Outside device site error n σ ellipsoids, therefore have uniquely away from r on ellipsoidcENearest point, corresponding λ are uniquely more than zero solution；
    Detector position error n σ ellipsoids are away from obstacle center rcMinimum range be：
    dc=| | rsE-rcE| |=| | rs-rc|| (12)
    Wherein
    Work as dc＞ R, represent that obstacle is integrally located at outside detector position error n σ ellipsoids, detector position error n σ ellipsoids are away from barrier The minimum range hindered is：
    de=dc-R (13)
    Work as dc≤ R, represent that detector position error n σ ellipsoids intersect with obstacle, it is ellipse that obstacle part is located at detector position error n σ Inside ball, minimum range d of the detector position error n σ ellipsoids away from obstacleeFor 0；
    Inside detector position error n σ ellipsoids or on surface, i.e., if step 4.2, obstacle are centrally located at：
    rcE TErcE≤1 (14)
    Then detector position error n σ ellipsoids are away from obstacle center rcMinimum range be 0；Correspondingly, obstacle is located in whole or in part Inside detector position error n σ ellipsoids, minimum range d of the detector position error n σ ellipsoids away from obstacleeFor 0；
    Minimum range d of the detector position error n σ ellipsoids away from obstacle obtained with described step 4.1 or step 4.2eSubtract control Safe distance d processeds, obtain safe distance desired value D of the detector with respect to obstacle：
    D=de-ds,de≥ds (15)
    Wherein control safe distance dsConsider the thrust spoke value including detector thruster configuration and each axial thrust device, control Control ability constraint including precision processed, value is preset according to detector configuring condition, to reflect detector control ability Constrain the influence to detector obstacle avoidance maneuverability；
    When minimum range of the detector position error n σ ellipsoids away from obstacle is less than control safe distance, safe distance desired value D For 0, i.e.,：
    D=0, de＜ ds (16)
    When detector is 0 with respect to the safe distance desired value of obstacle, the influence in state uncertainty and control constraints is represented Under, detector may collide with obstacle, and the security of detector now is relatively low；
    Step 5: the safe distance desired value obtained according to step 4 builds liapunov function；
    In the case where landing point connects firmly coordinate system, the potential field function phi on detector's status is builtq
    φq=xTQx (17)
    Wherein x=[x, y, z, vx,vy,vz]TFor detector's status variable, Q is with qi＞ 0, i=1 ..., 6 be cornerwise right Angular moment battle array；The potential field that above formula represents, the minimum point of existence anduniquess, is detector dbjective state x=0；As long as ensure detector The direction that state x is reduced along potential field is advanced, and detector's status automatic will level off to target landing state, i.e., while meet that target Land position and speed；
    According to safe distance desired value D of the detector obtained in step 4 with respect to obstacle, the potential field threatened on obstacle is built Function phih
    <mrow> <msub> <mi>&amp;phi;</mi> <mi>h</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> <msup> <mi>&amp;psi;e</mi> <mrow> <mo>-</mo> <msup> <msub> <mi>D</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>/</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </msup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>k</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, DiSafe distance desired value of the detector with respect to i-th of obstacle is represented, k represents the quantity of obstacle, ψ ＞ 0 and σ ＞ 0 For parameter；As safe distance desired value D of the detector with respect to obstacleiDuring reduction, potential field function phihValue increase；If the guidance of design The direction that rule makes detector and reduced along potential field is advanced, and detector will realize obstacle avoidance automatically；
    Finally, the liapunov function φ of following form is built：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>&amp;phi;</mi> <mo>=</mo> <msub> <mi>&amp;phi;</mi> <mi>q</mi> </msub> <mo>+</mo> <msub> <mi>&amp;phi;</mi> <mi>h</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msup> <mi>x</mi> <mi>T</mi> </msup> <mi>Q</mi> <mi>x</mi> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> <msup> <mi>&amp;psi;e</mi> <mrow> <mo>-</mo> <msup> <msub> <mi>D</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>/</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </msup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>k</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow>
    Liapunov function is by φqAnd φhTwo parts form so that detector dbjective state is unique global pole in potential field Small value point, and when detector is close to obstacle potential field value increase, as long as therefore design control acceleration instruction a make detector along gesture Field reduces direction and advanced, you can while realize autonomous obstacle avoidance and autonomous accurate soft landing；
    Step 6: design obstacle avoidance Guidance Law obtains the control acceleration a described in step 5, to realize autonomous obstacle avoidance With autonomous accurate soft landing.
  2. A kind of 2. place of safety expansion method of guidance of planetary landing obstacle avoidance as claimed in claim 1, it is characterised in that：
    Step 6 concrete methods of realizing is,
    The value of safe distance index D in step 4, selection perform step 6.1 or step 6.2, controlled accordingly Acceleration instructs a；
    Step 6.1, it is all higher than 0 when the safe distance desired value of relatively each obstacle of detector, i.e.,：
    Di＞ 0, i=1 ..., k (20)
    Order
    <mrow> <msub> <mi>a</mi> <mi>q</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mo>-</mo> <msub> <mi>q</mi> <mn>1</mn> </msub> <mi>x</mi> <mo>/</mo> <msub> <mi>q</mi> <mn>4</mn> </msub> <mo>-</mo> <msub> <mi>&amp;xi;</mi> <mi>x</mi> </msub> <mo>-</mo> <msub> <mi>g</mi> <mi>x</mi> </msub> <mo>-</mo> <mi>&amp;kappa;</mi> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>/</mo> <msub> <mi>q</mi> <mn>4</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>q</mi> <mn>2</mn> </msub> <mi>y</mi> <mo>/</mo> <msub> <mi>q</mi> <mn>5</mn> </msub> <mo>-</mo> <msub> <mi>&amp;xi;</mi> <mi>y</mi> </msub> <mo>-</mo> <msub> <mi>g</mi> <mi>y</mi> </msub> <mo>-</mo> <msub> <mi>&amp;kappa;v</mi> <mi>y</mi> </msub> <mo>/</mo> <msub> <mi>q</mi> <mn>5</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>q</mi> <mn>3</mn> </msub> <mi>z</mi> <mo>/</mo> <msub> <mi>q</mi> <mn>6</mn> </msub> <mo>-</mo> <msub> <mi>&amp;xi;</mi> <mi>z</mi> </msub> <mo>-</mo> <msub> <mi>g</mi> <mi>z</mi> </msub> <mo>-</mo> <msub> <mi>&amp;kappa;v</mi> <mi>z</mi> </msub> <mo>/</mo> <msub> <mi>q</mi> <mn>6</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>a</mi> <mi>h</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mstyle> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> </mstyle> <mo>(</mo> <mfrac> <mrow> <msub> <mi>&amp;psi;D</mi> <mi>i</mi> </msub> </mrow> <mrow> <msub> <mi>q</mi> <mn>4</mn> </msub> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>d</mi> <mrow> <mi>c</mi> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msup> <msub> <mi>D</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>/</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </msup> <mo>(</mo> <msub> <mi>x</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mstyle> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> </mstyle> <mo>(</mo> <mfrac> <mrow> <msub> <mi>&amp;psi;D</mi> <mi>i</mi> </msub> </mrow> <mrow> <msub> <mi>q</mi> <mn>5</mn> </msub> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>d</mi> <mrow> <mi>c</mi> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msup> <msub> <mi>D</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>/</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </msup> <mo>(</mo> <msub> <mi>y</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>c</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mstyle> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> </mstyle> <mo>(</mo> <mfrac> <mrow> <msub> <mi>&amp;psi;D</mi> <mi>i</mi> </msub> </mrow> <mrow> <msub> <mi>q</mi> <mn>6</mn> </msub> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>d</mi> <mrow> <mi>c</mi> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msup> <msub> <mi>D</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>/</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </msup> <mo>(</mo> <msub> <mi>z</mi> <mi>s</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>c</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>22</mn> <mo>)</mo> </mrow> </mrow>
    A=aq+ah (23)
    Wherein, κ is arithmetic number；And when target celestial body is small feature loss：
    <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;xi;</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;xi;</mi> <mi>y</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;xi;</mi> <mi>z</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mo>-</mo> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> <msub> <mi>v</mi> <mi>z</mi> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> <msub> <mi>v</mi> <mi>y</mi> </msub> <mo>+</mo> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> <mo>(</mo> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> <mi>x</mi> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <mi>z</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> <mo>(</mo> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <mi>y</mi> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> <mi>x</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <msub> <mi>v</mi> <mi>z</mi> </msub> <mo>+</mo> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <mo>(</mo> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <mi>y</mi> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> <mi>x</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> <mo>(</mo> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> <mi>z</mi> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> <mi>y</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <msub> <mi>v</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>+</mo> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> <mo>(</mo> <msub> <mi>&amp;omega;</mi> <mi>y</mi> </msub> <mi>z</mi> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> <mi>y</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <mo>(</mo> <msub> <mi>&amp;omega;</mi> <mi>z</mi> </msub> <mi>x</mi> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>x</mi> </msub> <mi>z</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mrow>
    Be kinetics equation (1) formula with x, y, the item relevant with spin angle velocity ω after the expansion of z-axis component form；Work as target celestial body For planet when, ξx=ξy=ξz=0；
    Step 6.2, when detector with respect to certain obstacle safe distance desired value be 0, that is, exist：
    Dj=0,1≤j≤k (25)
    Now the security of detector is relatively low；To ensure detector safety, start " state of emergency ", detector is promptly increased, It is corresponding control acceleration to instruct to be：
    A=[0,0, amax]T (26)
    Wherein amaxFor the thruster peak acceleration of z-axis positive direction.
  3. 3. a kind of place of safety expansion method of guidance of planetary landing obstacle avoidance as claimed in claim 1 or 2, its feature exist In：N values are depending on ellipsoid inflatable air area size requirement in described detector position error n σ ellipsoids, select the n values to be 3。
  4. A kind of 4. place of safety expansion method of guidance of planetary landing obstacle avoidance as claimed in claim 3, it is characterised in that：Step The rapid six acceleration instruction a that control asked for are analytical form, without complex calculations such as integrations, meet the real-time of online feedback control Property require.
  5. A kind of 5. place of safety expansion method of guidance of planetary landing obstacle avoidance as claimed in claim 4, it is characterised in that：Step The influence factor of obstacle avoidance track described in rapid four includes detector's status uncertain factor and control constraints factor.
  6. A kind of 6. place of safety expansion method of guidance of planetary landing obstacle avoidance, it is characterised in that：Landing solid point connection is defined first Coordinate system and error ellipsoid main shaft coordinate system；Landing kinetics equation is established in the case where landing point connects firmly coordinate system；According to detector Site error n σ ellipsoids determine the ellipsoid inflatable air area of detector, and then calculating detector is with respect to the safe distance index of obstacle Value；Liapunov function is built with respect to the safe distance desired value of obstacle based on detector's status and detector, utilizes Li Ya Pu Nuofu stability principles design obstacle avoidance Guidance Law, using acceleration instruction a control detector landing paths, reduce planet The influence that surface disturbs more, uncertain environment guides to detector obstacle avoidance, is effectively evaded to planetary surface obstacle, real Existing discretionary security precision landing.
  7. A kind of 7. place of safety expansion method of guidance of planetary landing obstacle avoidance as claimed in claim 6, it is characterised in that：Institute For n values depending on ellipsoid inflatable air area size requirement, it is 3 to select n values in the detector position error n σ ellipsoids stated.
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