CN107323692B - A kind of energy optimizing method of small feature loss soft landing avoidance - Google Patents
A kind of energy optimizing method of small feature loss soft landing avoidance Download PDFInfo
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Abstract
A kind of energy optimizing method of small feature loss soft landing avoidance disclosed by the invention, belongs to field of deep space exploration.The present invention obtains energy consumption as optimizing index to determine small feature loss soft landing energetic optimum Guidance Law, avoidance Guidance Law is obtained by regulating time parameter on the basis of energetic optimum Guidance Law, it can be guaranteed in landing mission according to avoidance Guidance Law, while detector and small feature loss surface do not collide, the energy consumption during avoidance is reduced to the maximum extent, to provide bigger energy margin for small feature loss soft landing, guarantee the security implementation of task.The technical problem to be solved in the present invention be guarantee lander can effective obstacle avoidance while, save energy consumption, ensure enough energy margins for small feature loss soft landing.
Description
Technical field
The present invention relates to a kind of energy optimizing methods of small feature loss soft landing avoidance, belong to field of deep space exploration.
Background technique
The following small feature loss landing detection mission is expected that by corresponding guidance technology, enables lander in scheduled landing
Point realizes accurate soft landing, that is, is conceived to the accuracy and safety of landing.
It lands for small feature loss safe, need to consider problem in terms of following two: 1, in landing mission, detector can
Effective obstacle avoidance, does not collide；2, it during avoidance, reduces energy consumption to the greatest extent, ensures enough energy margins.
The small feature loss soft landing avoidance guidance studied at present, the method for generalling use artificial potential function are marked by building
Amount potential function describes landform, by landing mission danger zone and touchdown area distinguish, guarantee that detector is landing
The safety of process is simultaneously realized in expected point of impact realization precision landing.But the avoidance method of guidance based on potential function is not examined sufficiently
The problem of considering energy consumption.
In order to ensure the safety of lander during small feature loss soft landing, it is necessary to be guided for small feature loss soft landing avoidance
This problem designs a kind of energy optimizing method of small feature loss soft landing avoidance, to guarantee that lander being capable of effective obstacle avoidance
While, energy consumption is reduced, ensures enough energy margins for small feature loss soft landing.
Summary of the invention
A kind of energy optimizing method technical problems to be solved of small feature loss soft landing avoidance disclosed by the invention are to guarantee
Lander can effective obstacle avoidance while, save energy consumption, ensure enough energy margins for small feature loss soft landing.
The purpose of the present invention is what is be achieved through the following technical solutions:
The energy optimizing method of a kind of small feature loss soft landing avoidance disclosed by the invention, using energy consumption as optimizing index
It obtains determining small feature loss soft landing energetic optimum Guidance Law, be obtained on the basis of energetic optimum Guidance Law by regulating time parameter
To avoidance Guidance Law, can be guaranteed in landing mission according to avoidance Guidance Law, what detector did not collided with small feature loss surface
Meanwhile the energy consumption during avoidance is reduced to the maximum extent, so that bigger energy margin is provided for small feature loss soft landing,
The security implementation of guarantee task.
A kind of energy optimizing method of small feature loss soft landing avoidance disclosed by the invention, includes the following steps:
Step 1: small feature loss soft landing energetic optimum Guidance Law is determined.
Under small feature loss inertial coodinate system, the kinetic model of lander is
Wherein, r=[x, y, z]TWith v=[vx,vy,vz]TRespectively position and speed vector；ω is small feature loss angle of rotation speed
Degree；A=[Tx,Ty,Tz]TRespectively three axis components of the detector control force acceleration under inertial system；
The vector expression of small feature loss gravitational acceleration respectively.Convenient for statement, formula (1) is abbreviated as
Since lander kinetic simulation pattern (2) is built upon under small feature loss inertial coodinate system, by initial time t0When,
Land point position coordinates are rf(t0), then in the moment t that landsfWhen, landing point position coordinates are rf(tf) be
Tip speed v (t of the lander relative to small feature loss is required when landingf) it is zero, then tip speed v (tf) in small day
It is under body inertial system
v(tf)=ω × rf(tf) (4)
The performance indicator of small feature loss soft landing energetic optimum is
Wherein, Γ is time parameter.Then Hamiltonian function is
Euler-Lagrange condition is
Governing equation is
Define tgo=tf- t is flight remaining time, then
It is then obtained by formula (8), control force acceleration a
A=-tgopr(tf)-pv(tf) (10)
State is expressed as
Therefore,
Formula (10) are brought into obtain
Known by formula (13), when solving tgoAfterwards, control force acceleration a is obtained, to obtain energetic optimum Guidance Law.For
This, bringing formula (8) into formula (6) has
Bringing formula (12) into formula (14) has
Therefore, tgoFor the positive root of reality of equation (16).
T is solved by formula (16)goAnd it brings formula (13) into and obtains small feature loss soft landing energetic optimum Guidance Law.
Step 2: judge whether to need to carry out avoidance according to navigation information.
Navigation system obtains small feature loss terrain information in real time, and terrain surface is denoted as
Geo (x, y, z)=0 (17)
In detector landing process, bring landing path (x (t), y (t), z (t)) into formula (17) left side, if it exists t <
tf, so that lander will collide with small feature loss, and method of guidance is transferred to step 3 when geo (x (t), y (t), z (t))≤0；
If t < tf, there is geo (x (t), y (t), z (t)) > 0 always, then will not collide, method of guidance return step one.
Step 3: design avoidance Guidance Law is joined according to the time that avoidance Guidance Law line solver obtains meeting avoidance requirement
Number Γ saves energy consumption to guarantee the effective obstacle avoidance of lander, ensures that enough energy are abundant for small feature loss soft landing
Degree.
Known by formula (16), tgoSolution will change with the change of time parameter Γ value.When time parameter Γ value
When change, the curvature of landing path is also changed correspondingly.Therefore Guidance Law can be achieved the purpose of obstacle avoidance with on-line control Γ value.
It is realized described in step 3 according to the preferably following method of avoidance Guidance Law line solver time parameter Γ:
Step 3.1: online Single-step Prediction is carried out to the landing path of lander.
When time parameter Γ is certain certain value, by formula (13), the acceleration a at k moment is obtainedk, and by the speed at k moment
vkWith acceleration akIt brings lander kinetic simulation pattern (2) into and carries out the position r that numerical integration obtains (k+1) moment(k+1)And speed
Spend v(k+1), and formula is carried it into tgoNumerical value be updated, bring into formula (13) obtain (k+1) moment acceleration a(k+1).From
And obtain the position r at (k+1) moment(k+1), speed v(k+1)With acceleration a(k+1), complete the online list to lander landing path
Step prediction.
Step 3.2: the landing path of online Single-step Prediction method on-line prediction lander described in step 3.1 is repeated, it will
Time parameter Γ is considered as the independent variable of collision equation (18), and the time parameter Γ for meeting avoidance requirement is obtained by formula (18),
To guarantee the effective obstacle avoidance of lander.
F (Γ)=geo (x, y, z；Γ)=0 (18)
Since the performance indicator formula (5) in step 1 is using energy consumption as optimizing index, obtain determining that small feature loss is soft
Land energetic optimum Guidance Law, step 3 obtain avoidance guidance by regulating time parameter Γ on the basis of energetic optimum Guidance Law
Rule, can save energy consumption while realizing effective obstacle avoidance, ensure that enough energy are abundant for small feature loss soft landing
Degree.
The utility model has the advantages that
A kind of energy optimizing method of small feature loss soft landing avoidance disclosed by the invention, for the first time draws the method for optimum control
Enter in small feature loss soft landing avoidance Design of Guidance Law, energy consumption is obtained to determine small feature loss soft landing energy as optimizing index
Optimal guidance law obtains avoidance Guidance Law by regulating time parameter Γ on the basis of energetic optimum Guidance Law, according to avoidance
Guidance Law can guarantee in landing mission, while detector and small feature loss surface do not collide, reduce keep away to the maximum extent
Energy consumption during barrier guarantees the security implementation of task to provide bigger energy margin for small feature loss soft landing.
Detailed description of the invention
Fig. 1 is the flow chart that the instruction of small feature loss soft landing avoidance method of guidance generates；
Fig. 2 is the curve for using with not using avoidance method of guidance relative altitude；
Fig. 3 is the partial enlargement curve for using with not using avoidance method of guidance relative altitude.
Specific embodiment
Objects and advantages in order to better illustrate the present invention, below with reference to one embodiment and respective drawings in invention
Appearance is described further.
Embodiment 1:
For the feasibility and beneficial effect for verifying the method for the present invention, the present embodiment is by taking Landing on Small Bodies Eros 433 as an example.
A kind of energy optimizing method of small feature loss soft landing avoidance, includes the following steps: disclosed in the present embodiment
Step 1: the form of small feature loss soft landing energetic optimum Guidance Law is determined.
Under small feature loss inertial coodinate system, the kinetic model of lander is
Wherein, r=[x, y, z]TWith v=[vx,vy,vz]TRespectively position and speed vector；
A=[Tx,Ty,Tz]TRespectively three axis components of the detector control force acceleration under inertial system；
The vector expression small feature loss spin velocity of small feature loss gravitational acceleration respectively
For ω=[0 0 ω]T, the spin velocity of 433 asteroid of Eros is taken as ω=3.3 × 10-4rad/s.It is convenient for statement,
Formula (19) is abbreviated as
Since lander kinetic simulation pattern (19) is built upon under small feature loss inertial coodinate system, by initial time t0When,
Landing point position coordinates are rf(t0), then in the moment t that landsfWhen, landing point position coordinates are rf(tf) be
Requirement lander is zero relative to the tip speed of small feature loss when landing, then tip speed v (tf) used in small feature loss
It is under property system
v(tf)=ω × rf(tf) (22)
Boundary condition is shown in Table 1
1 small feature loss soft landing boundary condition of table
| x,m | y,m | z,m | vx,m/s | vy,m/s | vz,m/s | |
| T=0 | 10177 | 6956 | 8256 | -25 | -12 | -17 |
| T=tf | 853 | 5010 | 45 | 0 | 0 | 0 |
The performance indicator of small feature loss soft landing energetic optimum is
Wherein, Γ is time parameter.Then Hamiltonian function is
Euler-Lagrange condition is
Governing equation is
Define tgo=tf- t is flight remaining time, then
It is then obtained by formula (26), control force acceleration a
A=-tgopr(tf)-pv(tf) (28)
State is expressed as
Therefore,
Formula (28) are brought into obtain
Known by formula (31), when solving tgoAfterwards, control force acceleration a is obtained, to obtain energetic optimum Guidance Law.For
This, bringing formula (26) into formula (24) has
Bringing formula (30) into formula (32) has
Therefore, tgoFor the positive root of reality of equation (33).
T is solved by formula (34)goAnd it brings formula (31) into and obtains small feature loss soft landing energetic optimum Guidance Law.
Step 2: judge whether to need to carry out avoidance according to navigation information.
Navigation system obtains small feature loss terrain information in real time, and terrain surface is denoted as
Geo (x, y, z)=0 (35)
In detector landing process, bring landing path (x (t), y (t), z (t)) into formula (35) left side, if it exists t <
tf, so that lander will collide with small feature loss, and method of guidance is transferred to step 3 when geo (x (t), y (t), z (t))≤0；
As t < tfWhen, there is geo (x (t), y (t), z (t)) > 0 always, then will not collide, method of guidance return step one.
Step 3: avoidance Design of Guidance Law, line solver time parameter Γ, thus guarantee the effective obstacle avoidance of lander,
Energy consumption is saved, ensures enough energy margins for small feature loss soft landing.
Known by formula (34), tgoSolution will change with the change of time parameter Γ value.When the change of Γ value,
The curvature of land track also changes correspondingly.Therefore Guidance Law can be achieved the purpose of obstacle avoidance with on-line control Γ value.
Following method is selected to realize according to avoidance Guidance Law line solver time parameter Γ described in step 3:
Step 3.1: online Single-step Prediction is carried out to the landing path of lander
When time parameter Γ is certain certain value, by formula (31), the acceleration a at available k momentk, and by the k moment
Speed vkWith acceleration akIt brings lander kinetic simulation pattern (19) into and carries out the position r that numerical integration obtains (k+1) moment(k+1)
With speed v(k+1), and formula (34) is carried it into tgoNumerical value be updated, bring into formula (13) obtain (k+1) moment acceleration
Spend a(k+1).To obtain the position r at (k+1) moment(k+1), speed v(k+1)With acceleration a(k+1), complete to lander landing path
Online Single-step Prediction.
Step 3.2: the landing path of online Single-step Prediction method on-line prediction lander described in step 3.1 is repeated, it will
Time parameter Γ is considered as the independent variable of collision equation (35), and the time parameter Γ for meeting avoidance requirement is obtained by formula (35),
To guarantee the effective obstacle avoidance of lander.
F (Γ)=geo (x, y, z；Γ)=0 (36)
Since the performance indicator formula (23) in step 1 is using energy consumption as optimizing index, obtain determining that small feature loss is soft
Land energetic optimum Guidance Law, step 3 obtain avoidance guidance by regulating time parameter Γ on the basis of energetic optimum Guidance Law
Rule, can save energy consumption while realizing effective obstacle avoidance, ensure that enough energy are abundant for small feature loss soft landing
Degree.
The present embodiment is verified with carrying out landing example in small feature loss Eros 433.Wherein, whole story position coordinates are initial
Coordinate when moment t=0 under inertial coodinate system, whole story speed are the speed relative to small feature loss.Fig. 2 and Fig. 3 are provided respectively
With and without avoidance Guidance Law, relative altitude versus time curve.As can be seen from Figure, it is not guided using avoidance
Under conditions of rule, there is negative value in relative altitude, i.e. lander is collided with small feature loss；After avoidance Guidance Law, entirely
In landing mission, relative altitude is always positive value, i.e. the lander obstacle that has effectively circumvented small feature loss surface.
Avoidance method of guidance is not used, and the energy consumption of whole process is 0.70125；It is whole after avoidance method of guidance
The energy consumption of a landing mission is 0.99225.
Above-described specific descriptions have carried out further specifically the purpose of invention, technical scheme and beneficial effects
It is bright, it should be understood that the above is only a specific embodiment of the present invention, the protection model being not intended to limit the present invention
It encloses, all within the spirits and principles of the present invention, any modification, equivalent substitution, improvement and etc. done should be included in the present invention
Protection scope within.
Claims (2)
1. a kind of energy optimizing method of small feature loss soft landing avoidance, it is characterised in that: include the following steps,
Step 1: small feature loss soft landing energetic optimum Guidance Law is determined；
Under small feature loss inertial coodinate system, the kinetic model of lander is
Wherein, r=[x, y, z]TWith v=[vx,vy,vz]TRespectively position and speed vector；ω is small feature loss spin velocity；a
=[Tx,Ty,Tz]TRespectively three axis components of the lander control force acceleration under inertial system；The vector expression of small feature loss gravitational acceleration respectively；Convenient for statement, formula (1) is abbreviated as
Since lander kinetic simulation pattern (2) is built upon under small feature loss inertial coodinate system, by initial time t0When, landing point
Position coordinates are rf(t0), then in the moment t that landsfWhen, landing point position coordinates are rf(tf) be
Tip speed v (t of the lander relative to small feature loss is required when landingf) it is zero, then tip speed v (tf) used in small feature loss
It is under property system
v(tf)=ω × rf (tf) (4)
The performance indicator of small feature loss soft landing energetic optimum is
Wherein, Γ is time parameter；Then Hamiltonian function is
Euler-Lagrange condition is
Governing equation is
Define tgo=tf- t is flight remaining time, then
It is then obtained by formula (8), control force acceleration a
A=-tgopr(tf)-pv(tf) (10)
State is expressed as
Therefore,
Formula (10) are brought into obtain
Known by formula (13), when solving tgoAfterwards, control force acceleration a is obtained, to obtain energetic optimum Guidance Law；For this purpose, will
Formula (8), which brings formula (6) into, to be had
Bringing formula (12) into formula (14) has
Therefore, tgoFor the positive root of reality of equation (16)；
T is solved by formula (16)goAnd it brings formula (13) into and obtains small feature loss soft landing energetic optimum Guidance Law；
Step 2: judge whether to need to carry out avoidance according to navigation information；
Navigation system obtains small feature loss terrain information in real time, and terrain surface is denoted as
Geo (x, y, z)=0 (17)
In lander landing mission, landing path (x (t), y (t), z (t)) is brought into formula (17) left side, if it exists t < tf, make
When obtaining geo (x (t), y (t), z (t))≤0, lander will collide with small feature loss, and method of guidance is transferred to step 3；If t <
tf, there is geo (x (t), y (t), z (t)) > 0 always, then will not collide, method of guidance return step one；
Step 3: design avoidance Guidance Law obtains the time parameter Γ for meeting avoidance requirement according to avoidance Guidance Law line solver,
To guarantee the effective obstacle avoidance of lander, energy consumption is saved, ensures enough energy margins for small feature loss soft landing.
2. a kind of energy optimizing method of small feature loss soft landing avoidance as described in claim 1, it is characterised in that: in step 3
Described selects following method to realize according to avoidance Guidance Law line solver time parameter Γ,
Step 3.1: online Single-step Prediction is carried out to the landing path of lander；
When time parameter Γ is certain certain value, by formula (13), the acceleration a at k moment is obtainedk, and by the speed v at k momentkWith
Acceleration akIt brings lander kinetic simulation pattern (2) into and carries out the position r that numerical integration obtains (k+1) moment(k+1)And speed
v(k+1), and formula (16) is carried it into tgoNumerical value be updated, bring into formula (13) obtain (k+1) moment acceleration a(k+1)；
To obtain the position r at (k+1) moment(k+1), speed v(k+1)With acceleration a(k+1), complete to the online of lander landing path
Single-step Prediction；
Step 3.2: the landing path of online Single-step Prediction method on-line prediction lander described in step 3.1 is repeated, by the time
Parameter Γ is considered as the independent variable of collision equation (18), and the time parameter Γ for meeting avoidance requirement is obtained by formula (18), thus
Guarantee the effective obstacle avoidance of lander；
F (Γ)=geo (x, y, z；Γ)=0 (18).
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