CN109696917A - A kind of spacecraft intersects barrier-avoiding method and system automatically - Google Patents
A kind of spacecraft intersects barrier-avoiding method and system automatically Download PDFInfo
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- CN109696917A CN109696917A CN201910080483.3A CN201910080483A CN109696917A CN 109696917 A CN109696917 A CN 109696917A CN 201910080483 A CN201910080483 A CN 201910080483A CN 109696917 A CN109696917 A CN 109696917A
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
- G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/10—Simultaneous control of position or course in three dimensions
- G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
Abstract
The invention discloses a kind of spacecrafts to intersect barrier-avoiding method and system automatically.The method includes Euler's distances most short under ellipsoid to solve, the building of target attraction potential function, the building of Obstacle avoidance potential function under sigmoid function, controller design based on speed artificial potential function and the sub-optimal velocity artificial potential function controller design based on the related Riccati equation of state.The present invention is suitable for the autonomous rendezvous avoidance obstacle of spacecraft, pass through Euler's determination of distance most short under ellipsoid, spacecraft and the distance between passive space vehicle or barrier can be more accurately calculated, so as to precisely control the path of spacecraft, reduces unnecessary fuel consumption；Sigmoid function is introduced into space industry to define Obstacle avoidance potential function for the first time simultaneously, to form overall potential function, and then design control law appropriate, can have more accurate flight path and faster response speed with track of more precise control spacecraft when far from barrier and close to barrier.
Description
Technical field
The present invention relates to the autonomous rendezvous technical fields of spacecraft, intersect avoidance side automatically more particularly to a kind of spacecraft
Method and system.
Background technique
From the last century 80's, units concerned just propose Orbital Express program, and wherein Orbital Express program is main
Meaning with following several respects:
(1) in the service life for extending satellite, the survival ability of satellite in orbit is improved.Orbital Express satellite have " self with
The ability of maintenance " and " mutual maintenance ", so as to greatly promote and extend survival ability and the longevity of satellite in orbit
Life；
(2) the following maintenance task is executed, accident satellite is saved.The coming years, the existing space shuttle in the U.S. will be moved back all
The task of labour, the future maintenance important in-orbit spacecraft in the U.S. has fallen on the novel spacecraft of " Orbital Express " etc naturally
On；
(3) the space operations ability of U.S. army's satellite is greatly promoted.Orbital Express satellite can be used as space operations machine
People captures enemy satellites in space.
Its key technology needed mainly has: track it is autonomous rendezvous with close, autonomous capture with dock, track is replaced singly
Member and assembling replacement system, it is seen then that primary key technology is Autonomous rendezvous and docking, and either satellite is used for military use
Satellite capture or each task spacecraft all may need in-orbit service, technique all plays very important
Effect.
Although also there is a certain distance with the developed countries such as U.S. in terms of space technology in China, in recent years
Carry out greatly developing for China's spacecraft cause, in-orbit service task and the relevant technologies are same with very heavy for China
Want meaning.
In order to extend spacecraft service life, enhancing system performance or carry out breakdown maintenance, need to carry out in-orbit push away to spacecraft
Into a series of in-orbit services such as the supply of the consumables such as agent, working medium and in-orbit module replacing.With extend in-orbit life-span, restore and
Expand in-orbit function, improve on-orbit performance and survival ability is target, Servicing spacecraft according to assignment instructions, in earth station or
Under the support of space platform, it is motor-driven to passive space vehicle running track to implement long-range orbital rendezvous, autonomous to complete to target space flight
The tracking measurement of device is approached and is stopped, thus passive space vehicle is repaired, is safeguarded, is upgraded, is fed or Auxiliary Track turn
It moves, improves in-orbit military satellite public system utilization rate, extend in-orbit service life, reduce the risk and cost of application.
The main target of Chinese Space in-orbit service are as follows: realize that spacecraft is overall, remote independent quickly intersects, space is non-
Cooperative target capture, tracking and form identification, weapon carry and the core keys such as rapid fire, in-orbit filling and module replacing
The important breakthrough of technology, in-orbit module replacing and repropellenting substantially can realize in-orbit system and service.Key skill therein
Art mainly includes the GN &C during orbit maneuver, and noncooperative target orbital rendezvous approaches and accompanying flying
Technology, accurate terminal guidance technology and orbit maneuver latter end posture fast and stable technology etc..Wherein spacecraft is autonomous rendezvous
It is most important to dock avoidance obstacle.
According to existing literature, autonomous rendezvous related ends can be summarized as two major classes.The first kind is primarily upon optimal reason
By key concept is to convert constrained optimization problem for avoidance problem, and solve with optimum theory.In addition, fuel oil
Cost is also regarded as performance indicator important in reference system.Intersection track is carried out using the thought of integral linear programming
Line optimization.Although optimum theory is widely used in autonomous rendezvous research, but still is come with some shortcomings.Seriously
The problem of be limit optimum theory application computation burden.Another kind of is the research of autonomous rendezvous analysis and Control strategy, is realized
Complexity is low, the control method of available analytical expression.Artificial potential function (artificial potential
Function, APF) it is used as a kind of typical analytic method, from gravitational field and electric field, with efficient, succinct expression way
It develops, is concerned.This method is proposed by Khatib first, and is applied to the path planning of ground robot.Then,
APF technology is introduced into space field, solves the problems, such as the McInnes maneuver autopilot autonomous rendezvous to spacecraft.In above-mentioned work
On the basis of work, APF is applied to the control of satellite formation flying and in-orbit assembly, in addition, APF is frequently used for controlling with other
Theory processed combines, to meet different mission requirements.For example, be directed to static-obstacle, propose a kind of new adaptive artificial
Potential function control law, and be further improved, precision is higher.A kind of dynamic based on artificial potential function and fuzzy control theory
Barrier evades mixing control method, is discussed on the basis of APF and sliding formwork control for satellites formation task.Separately
A kind of strategy is the attraction potential replaced in artificial potential function using linear quadratic regulator, and the avoidance for improving control algolithm is received
Hold back speed.For the formation of elliptical orbit satellite, LQR (linear quadratic regulator, linear quadratic have been formulated
Type adjuster)/APF control law, and verified on Mango satellite and Tango satellite.
However, the shortcomings that artificial potential function, is also very easy to find, these algorithms in fuel use aspect be not it is optimal,
They may include local minimum.In addition, the shape of extraterrestrial target is reduced to spherical shape, external envelope in above-mentioned achievement
It is not considered more accurate yet.If the three-dimensional dimension of spatial object is different, this simplified method will lead to the superfluous of spatial description
It is remaining.Therefore, above-mentioned limitation how to be overcome to become the emphasis of this field research.It is existing about Spacecraft Rendezvous control of collision avoidance
Research consider spherical form mostly to describe the external envelope of spacecraft and barrier, this is equivalent between boundary and mass center
Full-size.It is obvious that traditional method will cause the redundancy of barrier description, control precision is reduced.
Summary of the invention
The object of the present invention is to provide a kind of spacecrafts to intersect barrier-avoiding method and system automatically, is navigated with more precise control
The speed of its device and position converge on dbjective state point, reduce space trajectory error, reduce intersection process fuel consumption.
To achieve the above object, the present invention provides following schemes:
A kind of spacecraft intersects barrier-avoiding method automatically, which comprises
Obtain the position vector and desired locations vector of spacecraft；
Attract potential function according to the position vector and desired locations vector building target；
Obstacle avoidance potential function is constructed based on sigmoid function；
Potential function and the Obstacle avoidance potential function is attracted to determine overall potential function according to the target；
The control law based on speed artificial potential function is determined according to the overall potential function；
Attract potential function to carry out the optimization of state correlation Riccati equation the target according to the control law, obtains base
In the sub-optimal velocity artificial potential function controller of state correlation Riccati equation；
The flying speed and posture that the spacecraft is controlled using the sub-optimal velocity artificial potential function controller, make institute
It states spacecraft and reaches desired locations and avoiding barrier.
Optionally, described that potential function is attracted according to the position vector and desired locations vector building target, it is specific to wrap
It includes:
It is according to the position vector and desired locations vector building target attraction potential function
Wherein φaAttract potential function for target；R is the position vector of spacecraft；rfFor the desired locations vector of spacecraft；P is partly just
Set matrix.
Optionally, described that Obstacle avoidance potential function is constructed based on sigmoid function, it specifically includes:
Obtain the general type of the potential field function of the sigmoid functionWherein γ is barrier
Hinder the coverage of object, N is the surface number of barrier, SiFor the mathematic(al) representation in i-th of face of barrier；
Obtain relative position expression formula S (r, the r of the spacecraft Yu the barrier mass centero)=1- (r-ro)TMo(r-
ro)；Wherein S (r, ro) be spacecraft and barrier mass center relative position；R is the position vector of spacecraft；roIndicate obstacle
The substance heart；MoFor the information matrix of barrier；
According to describedWith relative position expression formula S (r, the ro)=1- (r-ro)TMo(r-ro)
Construct the Obstacle avoidance potential function
Wherein φrObstacle avoidance potential function for spacecraft relative to barrier；Most short Europe of the d between spacecraft and barrier
Draw distance； dctFor the distance of spacecraft centroid to desired locations；dotFor the distance of barrier mass center to desired locations；dsFor most
Small stop distance.
Optionally, described to attract potential function and the Obstacle avoidance potential function to determine total body posture letter according to the target
Number, specifically includes:
Potential function and the Obstacle avoidance potential function is attracted to determine the overall potential function according to the targetWherein φ is overall potential function；kaFor gravitational potential energy coefficient；krFor repulsion potential energy coefficient, φaFor
Target attracts potential function；For Obstacle avoidance potential function caused by i-th of barrier, m is the barrier around spacecraft
Number.
Optionally, described that the control law based on speed artificial potential function is determined according to the overall potential function, it is specific to wrap
It includes:
Determine that liapunov function is according to the overall potential functionWherein V is Lee
Ya Punuofu function；Gradient for overall potential function φ about Space Vehicle position vector r；For the speed of spacecraft；
First derivative is asked to the liapunov function, is obtainedWhereinFor Lee
The first derivative of Ya Punuofu function；H (φ) is the Hessian matrix of overall potential function φ；For the acceleration of spacecraft；
Ensure describedIt is negative, obtaining the control law based on speed artificial potential function isWherein uVAPFFor the control law based on speed artificial potential function；K
For positive definite matrix；For the output valve of Space Vehicle System output equation.
Optionally, described to attract potential function to carry out state correlation Riccati equation the target according to the control law
Optimization, obtains the sub-optimal velocity artificial potential function controller based on state correlation Riccati equation, specifically includes:
Ideal control law u is obtained according to correlated condition Riccati equation*(X)=- R (X)-1B(X)TE(X)X(t)；WhereinR and E is coefficient matrix；Wherein 03×3For 3 × 30 matrixes of dimension, I3×3For 3 × 3 dimension unit squares
Battle array；
According to the ideal control law u*(X)=- R (X)-1B(X)TE (X) X (t) determines the multitude of spacecraft dynamics equation
Card proposes formWhereinFor X's (t)
First derivative；For the optimal velocity of spacecraft；For the optimal acceleration of spacecraft； KSDRE(X)=R (X)-1B(X)TE
(X)；For coefficient matrix, wherein 03×3For 3 × 30 matrixes of dimension, I3×3For 3 × 3 dimension unit matrixs, A22For
MatrixWhereinFor the track angular speed of spacecraft；
WhereinFor the rail of spacecraft
Road angle angular speed；rcFor the orbit altitude of main spacecraft；μ is terrestrial gravitation constant；X, y and z is respectively r in three reference axis
On projection, i.e. r=[x, y, z]；rt=[(rc+x)2+y2+z2]1/2；
The Li Kati form of the spacecraft dynamics equation is subjected to abbreviation, obtains the optimal velocity of spacecraftOptimal accelerationWherein
Determine that target attracts the regulated quantity of potential function according to the optimal velocity and the optimal accelerationWhereinFor regulated quantity；N is coefficient matrix；It is expected position
Set rfDerivative；KMFor normal number；P is positive semidefinite matrix；
According to the regulated quantityIt adjusts the target and attracts potential function, to change the control law uVAPF, obtain institute
State the sub-optimal velocity artificial potential function controller based on state correlation Riccati equation.
A kind of spacecraft intersects obstacle avoidance system automatically, the system comprises:
Space Vehicle position vector obtains module, for obtaining the position vector and desired locations vector of spacecraft；
Target attracts potential function to construct module, for being inhaled according to the position vector and desired locations vector building target
Draw potential function；
Obstacle avoidance potential function constructs module, for constructing Obstacle avoidance potential function based on sigmoid function；
Overall potential function determining module, for attracting potential function and the Obstacle avoidance potential function according to the target
Determine totality potential function；
Control law determining module, for determining the control law based on speed artificial potential function according to the overall potential function；
State correlation Riccati equation optimization module, for according to the control law to the target attract potential function into
The optimization of row state correlation Riccati equation obtains the sub-optimal velocity artificial potential function control based on state correlation Riccati equation
Device；
Spacecraft intersects obstacle avoidance module automatically, for using described in sub-optimal velocity artificial potential function controller control
The flying speed and posture of spacecraft make the spacecraft reach desired locations and avoiding barrier.
Optionally, the target attracts potential function building module to specifically include:
Target attracts potential function construction unit, for being inhaled according to the position vector and desired locations vector building target
Drawing potential function isWherein φaAttract potential function for target；R is the position vector of spacecraft；rf
For the desired locations vector of spacecraft；P is positive semidefinite matrix.
Optionally, the Obstacle avoidance potential function building module specifically includes:
Sigmoid function acquiring unit, the general type of the potential field function for obtaining the sigmoid functionWherein γ is the coverage of barrier, and N is the surface number of barrier, SiIt is i-th of barrier
The mathematic(al) representation in face；
Relative position expression formula acquiring unit, for obtaining the relative position of the spacecraft Yu the barrier mass center
Expression formula S (r, ro)=1- (r-ro)TMo(r-ro)；Wherein S (r, ro) be spacecraft and barrier mass center relative position；R is
The position vector of spacecraft；roIndicate barrier mass center；MoFor the information matrix of barrier；
Obstacle avoidance potential function construction unit, for according toWith it is described
Relative position expression formula S (r, ro)=1- (r-ro)TMo(r-ro) the building Obstacle avoidance potential functionWherein φrFor spacecraft phase
For the Obstacle avoidance potential function of barrier；Most short Euler distance of the d between spacecraft and barrier； dctFor spacecraft
Distance of the mass center to desired locations；dotFor the distance of barrier mass center to desired locations；dsFor the smallest stop distance.
Optionally, the overall potential function determining module specifically includes:
Overall potential function determination unit, for attracting potential function and the Obstacle avoidance potential function according to the target
Determine the overall potential functionWherein φ is overall potential function；kaFor gravitational potential energy coefficient；krFor
Repulsion potential energy coefficient, φaAttract potential function for target；For Obstacle avoidance potential function caused by i-th of barrier, m is boat
Barrier number around its device.
The specific embodiment provided according to the present invention, the invention discloses following technical effects:
The present invention provides a kind of spacecraft and intersects barrier-avoiding method and system automatically, compared with traditional spherical surface describes method,
The spheroid that the present invention uses describes method and is more suitable for describing space and barrier.In addition, using sigmoid potential function as
Repulsive force carrys out avoiding obstacles, has the advantages that indicate arbitrary shape barrier potential field.On this basis, the present invention utilizes Lee
Ya Punuofu is theoretical, proposes and attracts the control of the speed artificial potential function of potential function and Obstacle avoidance potential function based on target
Method, it is ensured that the speed of spacecraft drops to zero before the outer layer for reaching barrier.On this basis, the present invention also mentions
A kind of riccati equation (state dependent Riccati equation, SDRE) based on State-dependence is gone out most
Dominant strategy, the strategy is optimal by shaping parameter progress of the adaptive algorithm to attractive artificial potential function, to increase by one
The optimality for determining degree solves the problems, such as that artificial potential function in fuel use aspect is not optimal.Therefore it is provided using the present invention
Spacecraft intersect barrier-avoiding method and system automatically, the speed and position for capableing of more precise control spacecraft converge on target
State point reduces space trajectory error, reduces the fuel consumption of intersection process.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be in embodiment
Required attached drawing is briefly described, it should be apparent that, the accompanying drawings in the following description is only some realities of the invention
Example is applied, it for those of ordinary skill in the art, without any creative labor, can also be according to these
Attached drawing obtains other attached drawings.
Fig. 1 is the method flow diagram that spacecraft provided by the invention intersects barrier-avoiding method automatically；
Fig. 2 is the inventive concept schematic diagram that spacecraft provided by the invention intersects barrier-avoiding method automatically；
Fig. 3 is the most short Euler of elliposoidal provided by the invention apart from schematic diagram；
Fig. 4 be it is provided by the invention based on the controller of speed artificial potential function under Spacecraft Rendezvous trajectory diagram；
Fig. 5 is under the sub-optimal velocity artificial potential function controller provided by the invention based on state correlation Riccati equation
Spacecraft Rendezvous trajectory diagram；
Fig. 6 is the fuel consumption comparison diagram of two kinds of controllers during spacecraft Autonomous rendezvous and docking；
Fig. 7 is the system construction drawing that spacecraft provided by the invention intersects obstacle avoidance system automatically.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts it is all its
His embodiment, shall fall within the protection scope of the present invention.
The object of the present invention is to provide a kind of spacecrafts to intersect barrier-avoiding method and system automatically, is navigated with more precise control
The speed of its device and position converge on dbjective state point, reduce space trajectory error, reduce intersection process fuel consumption.This
Invention provide a kind of automatic intersection barrier-avoiding method based on sub-optimal velocity artificial potential function include: under ellipsoid most short Euler away from
From solution, target attracts the building of potential function, the building of potential field function under Sigmoid function, barrier under sigmoid function
The building for hiding potential function, controller design based on speed artificial potential function and time based on the related Riccati equation of state
Excellent speed artificial potential function controller design.
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, with reference to the accompanying drawing and specific real
Applying mode, the present invention is described in further detail.
Fig. 1 is the method flow diagram that spacecraft provided by the invention intersects barrier-avoiding method automatically.Fig. 2 provides for the present invention
Spacecraft intersect the inventive concept schematic diagram of barrier-avoiding method automatically.Referring to Fig. 1 and Fig. 2, the present invention includes target attraction potential letter
Number, Obstacle avoidance potential function under potential field function, sigmoid function under Sigmoid function, based on speed artificial potential function
For controller to the sub-optimal velocity artificial potential function controller based on the related Riccati equation of state, two be directed to are ellipse
The distance between sphere requires most short Euler proposed by the present invention and solves apart from method for solving.
Fig. 3 is the most short Euler of elliposoidal provided by the invention apart from schematic diagram.The present invention derives most short between two ellipsoids
The representation of Euler's distance, as shown in figure 3, approximately regarding spacecraft and barrier as two spheroid E respectivelycAnd Eo,
xcyczcAnd x0y0z0Respectively space vehicle coordinates system and barrier coordinate system, r1 *And r2 *Respectively point on spacecraft and barrier
Coordinate, it is assumed that point r1 *WithThe distance between be most short Euler's distance, the spheroid for indicating spacecraft is transformed to one first
The sphere of a unit, the calculation formula of distance is under new coordinate systemWhereinAccording to lagrange's method of multipliers, r1 *Seat
It is designated asλ1For Lagrange multiplier, while we define matrix:
WhereinIf λ1Equal to DcCharacteristic value in minimum value, r1 *It can redefine are as follows:
Similarly under barrierCoordinate representation are as follows:
Define matrixWherein
The expression formula of most short Euler's distance at this time are as follows:
λ in formula1、λ2For Lagrange multiplier, r is the position vector of spacecraft.Subscript o, c of each parameter generation respectively
Table barrier and spacecraft, such as roFor the mass center of barrier；rcFor the mass center of spacecraft；MoFor the information matrix of barrier, represent
The actual size of barrier；McFor the information matrix of spacecraft, the actual size of spacecraft is represented.I is unit matrix, T
For to Matrix Calculating transposition, dependent variable, which is variable defined in calculating process, to be asked by the above-mentioned variable indicated
?.
Then, by the interative computation to formula (3), most short Euler's distance between spacecraft and barrier is found out.
On this basis, it is first determined the main thought of the artificial potential function of system, artificial potential function method is as follows: first
A scalar potential function is first defined, this potential function reflects the environment of entire state space, that is, the potential function defined is desired
State position has global minimum, and the restrictive condition of motion path is indicated with the region with higher potential function value, such as
Barrier, prohibited area or close to corridor etc., wherein the gradient value in high level potential function region directly reflect be applied to it is controlled
Hide the repulsion size in this region on object.And then control law appropriate is designed, make the derivative negative definite of potential function, so just
It can ensure that the position and speed of controlled device converges on desired dbjective state using Lyapunov stability theory
Point, and without prejudice to path restrictive condition.Artificial potential function method of guidance is actually a kind of method based on potential energy, it make by
Control object moves to low-potential energy position from high potential energy position, if pictute, moves on curved surface just as bead, can be from
Higher position moves to lower position, if having on path protrusion barrier, bead will cut-through object continue to
Lower position movement, overall potential function a part of system are named as target and attract potential function, it makes controlled device move to mesh
Punctuate, even if being controlled state motion to expectation state.Another part is named as Obstacle avoidance potential function, this part makes to be controlled
Object keeps off barrier, even if controlled state does not enter the high gesture region limited.After determining this thought, first definition is
The target attraction potential potential function of system, then the Obstacle avoidance potential function constructed by sigmoid function, form the totality of system
Potential function designs suitable non-linear liapunov function and solves control at this time under the premise of ensuring that its is minus
System rule, the controller as proposed by the present invention based on speed artificial potential function, while utilizing state correlation Riccati equation
Attract the parameter of potential function to optimize target, obtains the control law with some superiority, it is as proposed by the present invention to be based on
The sub-optimal velocity artificial potential function controller of state correlation Riccati equation.
Based on inventive concept shown in Fig. 2 and principle, spacecraft provided by the invention intersects barrier-avoiding method automatically and specifically wraps
It includes:
Step 101: obtaining the position vector and desired locations vector of spacecraft.
Step 102: potential function is attracted according to the position vector and desired locations vector building target.
Spacecraft will be by controller plc direction, acceleration etc., by entire spacecraft flight ring in flight course
A potential field is regarded in border as, and spacecraft controls spacecraft to gtoal setting by the attraction of target between target with intersecting, and passes through
Obstacle avoidance potential function between barrier and spacecraft controls spacecraft avoiding obstacles.So entire total body posture letter
Number includes two parts, and a part is that target attracts potential function, and another part is Obstacle avoidance potential function.According to potential field theorem,
The target attraction potential function representation of system are as follows:
Wherein φaAttract potential function for target, subscript a is attractive abbreviation, represents attraction.On in formula
Footmark T represents Matrix Calculating transposition.R is the position vector of spacecraft, rfIt is expected position vector (i.e. target position), P is partly just
Set matrix.
Step 103: Obstacle avoidance potential function is constructed based on sigmoid function.
Sigmoid potential function is introduced, the system potential function general type based on sigmoid function is derived, according to
The characteristic of sigmoid function introduces sigmoid function in Spacecraft Rendezvous for the first time, and obtains based on sigmoid letter
The general type of several potential field functions:
Wherein φrFor Obstacle avoidance potential function, the general type of sigmoid potential function is represented herein, and subscript r is
Repulsive abbreviation, indicates the meaning repelled.γ is the coverage of barrier, and N is the surface number of barrier, SiIt is i-th
The mathematic(al) representation in a face, works as SiWhen=0, the potential field value of the point on curved surface is 0.5, Si> 0, potential field value level off to 1, Si< 0,
Potential field value levels off to 0.
The present invention is that its performance is good using the purpose of the potential field function based on sigmoid function, and sigmoid function can
The more accurately two-dimentional three-dimensional structure of description object, and calculation amount is small, single order and the continuously differentiable property of high-order, guarantees
The continuity of power.Obstacle avoidance potential function based on sigmoid construction of function, amplitude and application range can pass through
The parameter for adjusting sigmoid function is adjusted.Below based on sigmoid function, derive based on sigmoid gesture letter
Count the expression for hindering object to hide potential function of general type.
Since give system potential function typicallys represent form (5), this premise is utilized to derive Obstacle avoidance gesture letter
Number, according to the formula (r-r of spheroidi)TMi(r-ri)=1, the relative position of spacecraft and barrier mass center be expressed as S (r,
ro)=1- (r-ro)TMo(r-ro), then by S (r, ro) be updated in formula (5), even Si=S (r, ro), it obtains:
Wherein φrObject is hindered to hide potential function relative to ellipsoid barrier for spacecraft, r is the position of spacecraft
Set vector, ri,MiRespectively mass center and ellipsoid range, i can be o or c, respectively represent barrier and spacecraft mass center and
Size.S(r,ro) be spacecraft and barrier mass center relative position, as S (r, ro) > 0 when, φrValue level off to 1, boat
The mass center of its device is in barrier ellipsoid shell, as S (r, roWhen)=0, φrValue level off to 0.5, the mass center of spacecraft is hindering
Hinder on object ellipsoid shell, as S (r, ro) < 0 when, φrValue level off to 0, the mass center of spacecraft is outside barrier ellipsoid shell.
dctAnd dotThe respectively distance of spacecraft centroid and barrier mass center to target position, dsFor the smallest stop distance,amaxFor peak acceleration, vcoIt, can be with by the formula (3) for the relative velocity of spacecraft and barrier
It acquiresWhereinThe respectively speed of spacecraft and barrier.
Step 104: attracting potential function and the Obstacle avoidance potential function to determine overall potential function according to the target.
If φ is the overall artificial potential function of whole system, a part is named as target and attracts potential function, it to be controlled
Object moves to target point (desired locations), even if being controlled state motion to expectation state.Another part is named as barrier and hides
Potential function is kept away, this part makes controlled device keep off barrier, even if controlled state does not enter the high gesture region limited.And
System totality potential function is this two-part adduction, i.e., the described target attracts potential function (4) and the Obstacle avoidance gesture letter
The adduction of number (6):
Wherein φ is overall potential function, i.e., space locating for spacecraft is seen as a potential field, and overall potential function is space flight
Total potential energy that device is subject in potential field, the repulsion of attraction and barrier including passive space vehicle.It is available according to potential function
The potential energy of spacecraft position, so that spacecraft is moved from high potential energy to low-potential energy direction.ka、krRespectively gravitational potential energy system
Several and repulsion potential energy coefficient, ka> 0, kr> 0.For Obstacle avoidance potential function caused by i-th barrier, m is surrounding barrier
Hinder object number.
Step 105: the control law based on speed artificial potential function is determined according to the overall potential function.
The most short Euler between spacecraft and barrier obtained by abovementioned steps apart from expression formula (3), spacecraft
Target attracts potential function (4) and Obstacle avoidance potential function (6), can derive based on speed artificial potential function controller
Expression formula, the specific steps are as follows:
Since kinematics model when spacecraft is autonomous rendezvous is nonlinear system, non-linear Lyapunov's theory can
To be used to design avoidance obstacle rule.In order to ensure Servicing spacecraft will not bump against during entire intersection with barrier, service
The relative velocity of spacecraft must be decreased to zero, then get to the outer layer of barrier.Therefore, the Li Yapu of system is selected
Promise husband's function are as follows:
WhereinFor the derivative about the time of Space Vehicle position, the i.e. speed of spacecraft,It is potential field φ about position
The gradient of vector r, derivation formula are as follows:
Wherein ka、krRespectively gravitational potential energy coefficient and repulsion potential energy coefficient,For obstacle caused by i-th of barrier
Object hides potential function；P is positive semidefinite matrix, roiFor the mass center of i-th of barrier, Si(r,roi) it is spacecraft and i-th of obstacle
The relative distance of object, MoiFor the information matrix of i-th of barrier.Gradient for potential field φ about position vector r, m are barrier
Hinder object quantity；rfFor target position (desired locations) vector.
First derivative is asked to liapunov function, is obtained:
Wherein H (φ) is the Hessian matrix of potential field φ, mathematical form are as follows:
First derivative is that the condition that Liapunov stability is set up is only when first derivative is less than zero, V positive definite
System Asymptotic Stability.So constructing control law u to meet above-mentioned conditionVAPFSo that above-mentioned condition is set up.Therefore in secondary control
Restrain uVAPFUnder, system asymptotically stable in the large.
EnsureIt is negative, obtains the control law based on speed artificial potential function are as follows:
Wherein K is positive definite matrix, and by uVAPFIt is brought intoIn,It sets up.
For the output valve of Space Vehicle System output equation.
Control law, that is, controller output quantity, for control spacecraft movement, the present invention design based on the artificial gesture of speed
The control law u of functionVAPFFor a kind of controller design thinking proposed by the present invention, subsequent step introduces state phase to the method
It closes Riccati equation to improve, with improving performance.
Step 106: attracting potential function to carry out state correlation Riccati equation the target according to the control law excellent
Change, obtains the sub-optimal velocity artificial potential function controller based on state correlation Riccati equation.
According to speed artificial potential function control law obtained in the step 105, to the target in its overall potential function
Attract potential function to carry out the optimization of state correlation Riccati equation, obtains the sub-optimal velocity people based on state correlation Riccati equation
Work potential function controller design, operating procedure are as follows:
Over time, if control law about the integral of time and the position of spacecraft as system performance index,
Equation are as follows:
WhereinFor performance index function；U is control input；Q≥0,R
>=0 is coefficient matrix.
Ideal control law is obtained according to correlated condition Riccati equation:
u*(X)=- R (X)-1B(X)TE(X)X(t) (14)
WhereinR and E is coefficient matrix；Matrix B (X) isWherein 03×3For 3 × 3 dimensions 0
Matrix, I3×3For 3 × 3 dimension unit matrixs；X (t) is a vector, its value is
In X ≠ 0, matrix E (X) positive definite and satisfaction:
E(X)A(X)+A(X)E(X)+Q(X)-E(X)B(X)R(X)-1B(X)TE (X)=0 (15)
Therefore, the closed loop power equation of nonlinear system can be rewritten are as follows:
If KSDRE(X)=R (X)-1B(X)TE (X), the optimal velocity and acceleration of spacecraftIt can lead to respectively
Following equation is crossed to acquire:
WhereinFor coefficient matrix, wherein 03×3For 3 × 30 matrixes of dimension, I3×3For 3 × 3 dimension units
Matrix, A22For matrixWhereinFor the track angular speed of spacecraft；
WhereinFor spacecraft
Track angle angular speed；rcFor the orbit altitude of main spacecraft；μ is terrestrial gravitation constant；X, y and z is respectively that r is sat in spacecraft
Mark the projection in three reference axis of system, i.e. r=[x, y, z]；rt=[(rc+x)2+y2+z2]1/2；
The present invention then passes through correlation according to the content of correlated condition Riccati equation, first setting target function (13)
It is (14) that state Riccati equation theorem, which obtains optimal control law, wherein KSDRE(X)=R (X)-1B(X)TE (X) can also be in the hope of
, formula (15) is Riccati equation constraint condition, acquires formula (14) and K by formula (15)SDRE(X), formula (16) is
The Li Kati form of spacecraft dynamics equation is used and utilizes u*(X) and KSDRE(X) spacecraft dynamics equation is replaced
It obtains formula (16), formula (17) is the abbreviation form of formula (16).The purpose for introducing Riccati equation is to spacecraft
Kinetics equation optimizes, and obtains formula (17), obtains optimal spacecraft velocity and acceleration by formula 17.It improves
Based on the controller of speed artificial potential function, so that its negative gradientWith optimal velocityIt is equal, reach more preferably control effect
Fruit.Suitable gravity coefficient P is designed below, it, can be with so the P obtained by optimal velocity since P belongs to total potential function φ
So thatIt is equal with optimal velocity, reach more preferably control effect.
It is only to attract the shaping parameter of artificial potential function to carry out target in the case where not considering barrier
Optimization, has obtained optimal solution.When spacecraft is far from barrier, target attracts potential field spacecraft can be driven to approach ideal velocityWhen spacecraft encounters barrier, barrier potential field can make spacecraft slow down and far from barrier, when far from after spacecraft
Ideal velocity can be converged on againTherefore the matrix P in potential function (4) is attracted to the target, carries out cholesky point
Solution:
Wherein each ρijIt is a parameter about the time, after arrangement:
Define error termTo the derivative of its seeking time:
In order to acquireBy above formula (20) be converted intoRelevant formula:Its
InMatrix N are as follows:
WhereinFor the parameter ρ obtained after decompositionijThe element that its derivation is obtained
It is worth, the position in subscript homography, matrix N is the coefficient matrix after formula (20) arrange, nijFor matrix N the i-th row jth column
Element, such as n11Correspond to the element value that matrix is located at 1 × 1 position.R is Space Vehicle position, riFor the element of the i-th row of r；
For the derivative of target position, rfiFor desired locations rfThe element of i-th row, such as rf3Represent rfThird row element, other phases
With expression.The analytical form that P is found out by formula (18)-(19), facilitates the update of P, formula (20), (21) be define it is optimal
Generalized error between speed and gravitational potential function negative gradient, is then derivedAnalytical form.
IfRight side be equal to-KMeop, it obtains:
Wherein KMFor normal number.
Above formula (22) is updated toIn, it obtainsSoWithError exponentially successively decrease, finally level off to zero, potential field finally made to level off to most about the negative gradient of position
Excellent speed.Due to P=ρTρ, so willIt is brought into the target
Attract potential function (4), to change the control law function (12), has just obtained time based on state correlation Riccati equation
Excellent speed artificial potential function controller.
Target attracts potential function to belong to overall potential function, and control law is designed by overall potential function, so passing through
It solvesP is obtained, P influences target again and attracts potential function (4), to change whole potential function, to influence control law.
Step 107: the flying speed and appearance of the spacecraft are controlled using the sub-optimal velocity artificial potential function controller
State makes the spacecraft reach desired locations and avoiding barrier.
The jet pipe of controller control spacecraft reaches specified mesh to change the flying speed and posture of spacecraft
Cursor position, and avoiding barrier realize that spacecraft intersects avoidance automatically.
Fig. 4 be it is provided by the invention based on the controller of speed artificial potential function under Spacecraft Rendezvous trajectory diagram.Fig. 5
For Spacecraft Rendezvous rail under the sub-optimal velocity artificial potential function controller provided by the invention based on state correlation Riccati equation
Mark figure.The flight path of the spacecraft under the controller control of speed artificial potential function proposed by the present invention is described in Fig. 4,
The task of spacecraft is to reach designated position from initial position in Fig. 4, is during which independently hidden to barrier, three small figures
Show respectively spacecraft in avoiding barrier between barrier at a distance from.Fig. 4 proves to be based on using proposed by the present invention
The controller of speed artificial potential function can complete the autonomous rendezvous avoidance task of spacecraft.It and is to the artificial gesture letter of speed in Fig. 5
Space flight under the sub-optimal velocity artificial potential function controller based on state correlation Riccati equation that several controllers optimizes
The running track of device again in the same circumstances, while also showing the safe distance between spacecraft and barrier.Due to space flight
Device is closer with obstacle distance, then the direction effect for needing spacecraft itself to provide is bigger, and fuel expends just more greatly, so
Sub-optimal velocity artificial potential function controller's effect proposed by the present invention based on state correlation Riccati equation is more preferable.Fig. 6 is boat
The fuel consumption comparison diagram of two kinds of controllers during its device Autonomous rendezvous and docking is to two kinds of controllers proposed by the present invention
The VAPFC and SVAPFC fuel consumption comparison in the flight course of 3000s in the same circumstances.VAPFC, which is represented, is based on speed people
The controller of work potential function, SVAPFC represent the sub-optimal velocity artificial potential function controller based on state correlation Riccati equation.
Fig. 6 horizontal axis is the time, and the longitudinal axis is fuel consumption, and curve 601 is that VAPFC controls lower spacecraft in the flight of 3000s in Fig. 6
Fuel consumption curve in journey, curve 602 are that SVAPFC controls lower spacecraft fuel consumption curve in the flight course of 3000s.
As it can be seen that being capable of high degree using the sub-optimal velocity artificial potential function controller the present invention is based on state correlation Riccati equation
Reduce fuel consumption.
The present invention also provides a kind of spacecrafts to intersect obstacle avoidance system automatically, and Fig. 7 is that spacecraft provided by the invention is handed over automatically
Can obstacle avoidance system system construction drawing, referring to Fig. 7, the system comprises:
Space Vehicle position vector obtains module 701, for obtaining the position vector and desired locations vector of spacecraft；
Target attracts potential function to construct module 702, for constructing target according to the position vector and desired locations vector
Attract potential function；
Obstacle avoidance potential function constructs module 703, for constructing Obstacle avoidance potential function based on sigmoid function；
Overall potential function determining module 704, for attracting potential function and the Obstacle avoidance gesture letter according to the target
Number determines overall potential function；
Control law determining module 705, for determining the control based on speed artificial potential function according to the overall potential function
Rule；
State correlation Riccati equation optimization module 706, for attracting potential function to the target according to the control law
The optimization of carry out state correlation Riccati equation, obtains the sub-optimal velocity artificial potential function control based on state correlation Riccati equation
Device processed；
Spacecraft intersects obstacle avoidance module 707 automatically, for controlling institute using the sub-optimal velocity artificial potential function controller
The flying speed and posture for stating spacecraft make the spacecraft reach desired locations and avoiding barrier.
Wherein, the target attracts potential function building module 702 to specifically include:
Target attracts potential function construction unit, for being inhaled according to the position vector and desired locations vector building target
Drawing potential function isWherein φaAttract potential function for target；R is the position vector of spacecraft；rf
For the desired locations vector of spacecraft；P is positive semidefinite matrix.
The Obstacle avoidance potential function building module 703 specifically includes:
Sigmoid function acquiring unit, the general type of the potential field function for obtaining the sigmoid functionWherein γ is the coverage of barrier, and N is the surface number of barrier, SiIt is i-th of barrier
The mathematic(al) representation in face；
Relative position expression formula acquiring unit, for obtaining the relative position of the spacecraft Yu the barrier mass center
Expression formula S (r, ro)=1- (r-ro)TMo(r-ro)；Wherein S (r, ro) be spacecraft and barrier mass center relative position；R is
The position vector of spacecraft；roIndicate barrier mass center；MoFor the information matrix of barrier；
Obstacle avoidance potential function construction unit, for according toAnd institute
State relative position expression formula S (r, ro)=1- (r-ro)TMo(r-ro) the building Obstacle avoidance potential functionWherein φrFor spacecraft phase
For the Obstacle avoidance potential function of barrier；Most short Euler distance of the d between spacecraft and barrier； dctFor spacecraft
Distance of the mass center to desired locations；dotFor the distance of barrier mass center to desired locations；dsFor the smallest stop distance.
The totality potential function determining module 704 specifically includes:
Overall potential function determination unit, for attracting potential function and the Obstacle avoidance potential function according to the target
Determine the overall potential functionWherein φ is overall potential function；kaFor gravitational potential energy coefficient；krFor
Repulsion potential energy coefficient, φaAttract potential function for target；For Obstacle avoidance potential function caused by i-th of barrier, m is boat
Barrier number around its device.
The control law determining module 705 specifically includes:
Liapunov function determination unit, for determining that liapunov function is according to the overall potential functionWherein V is liapunov function；For overall potential function φ about Space Vehicle position to
Measure the gradient of r；For the speed of spacecraft；
Derivation unit is obtained for seeking first derivative to the liapunov function
WhereinFor the first derivative of liapunov function；H (φ) is the Hessian matrix of overall potential function φ；For spacecraft
Acceleration；
Control law determination unit, it is described for ensuringIt is negative, obtains the control law based on speed artificial potential function
ForWherein uVAPFFor the control law based on speed artificial potential function；
K is positive definite matrix；For the output valve of Space Vehicle System output equation.
The state correlation Riccati equation optimization module 706 specifically includes:
Ideal control law determination unit, for obtaining ideal control law u according to correlated condition Riccati equation*(X)=- R
(X)-1B(X)TE(X)X(t)；WhereinR and E is coefficient matrix；Wherein 03×3For 3 × 3 dimensions 0
Matrix, I3×3For 3 × 3 dimension unit matrixs；
Spacecraft dynamics equation Li Kati form determination unit, for according to the ideal control law u*(X)=- R
(X)-1B(X)TE (X) X (t) determines the Li Kati form of spacecraft dynamics equation
WhereinIt is led for the single order of X (t)
Number；For the optimal velocity of spacecraft；For the optimal acceleration of spacecraft；
For coefficient matrix, wherein 03×3For 3 × 3 dimensions 0
Matrix, I3×3For 3 × 3 dimension unit matrixs, A22For matrixWhereinFor the track angle speed of spacecraft
Rate；A21Expression formula be
WhereinFor the track angle angular speed of spacecraft；rcFor the orbit altitude of main spacecraft；μ is terrestrial gravitation constant；
X, y and z is respectively projection of the r in three reference axis, i.e. r=[x, y, z]； rt=[(rc+x)2+y2+z2]1/2；
Abbreviation unit obtains spacecraft for the Li Kati form of the spacecraft dynamics equation to be carried out abbreviation
Optimal velocityOptimal accelerationWherein
Target attracts potential function regulated quantity determination unit, for true according to the optimal velocity and the optimal acceleration
It sets the goal and attracts the regulated quantity of potential functionWhereinTo adjust
Section amount；N is coefficient matrix；For desired locations rfDerivative；KMFor normal number；
P is positive semidefinite matrix；
Sub-optimal velocity artificial potential function controller determination unit, for according to the regulated quantityThe target is adjusted to inhale
Draw potential function, to change the control law uVAPF, it is artificial to obtain the sub-optimal velocity based on state correlation Riccati equation
Potential function controller.
To sum up, compared with prior art, the present invention at least having following advantage:
1, relative to traditional spherical representation, elliposoidal representation proposed by the present invention is to spacecraft and barrier
Description is more accurate and real, provides good mathematical model for controller design of the invention.
2, sigmoid function is introduced into space industry by relatively traditional artificial potential function, the present invention for the first time,
Sigmoid function can more accurately describe the two-dimentional three-dimensional structure of object, and calculation amount is small, and single order and high-order are continuous
Property that can be micro-, ensure that the continuity of power, and based on the potential function of sigmoid construction of function, amplitude and application range can be with
Parameter by adjusting sigmoid function is adjusted.
3, the overall potential function for establishing system in the present invention based on ellipsoidal model, makes spacecraft hide barrier by repulsion
Hinder, when spacecraft reaches barrier periphery, relative velocity is reduced to zero, is based on according to the building of non-linear liapunov function
The artificial potential function controller of speed can more accurately control spacecraft avoiding barrier, reach intersection place.
4, state correlation Riccati equation is utilized in the present invention, attracts the parameter in potential function to carry out aims of systems excellent
Change, make it have optimality to a certain extent, be capable of the intersection track of more precise control spacecraft, reduces fuel consumption.
Each embodiment in this specification is described in a progressive manner, the highlights of each of the examples are with its
The difference of his embodiment, the same or similar parts in each embodiment may refer to each other.For being disclosed in embodiment
For system, since it is corresponded to the methods disclosed in the examples, so being described relatively simple, related place is referring to method portion
It defends oneself bright.
Used herein a specific example illustrates the principle and implementation of the invention, above embodiments
Illustrate to be merely used to help understand method and its core concept of the invention；At the same time, for those skilled in the art,
According to the thought of the present invention, there will be changes in the specific implementation manner and application range.In conclusion this specification
Content should not be construed as limiting the invention.
Claims (10)
1. a kind of spacecraft intersects barrier-avoiding method automatically, which is characterized in that the described method includes:
Obtain the position vector and desired locations vector of spacecraft；
Attract potential function according to the position vector and desired locations vector building target；
Obstacle avoidance potential function is constructed based on sigmoid function；
Potential function and the Obstacle avoidance potential function is attracted to determine overall potential function according to the target；
The control law based on speed artificial potential function is determined according to the overall potential function；
Attract potential function to carry out the optimization of state correlation Riccati equation the target according to the control law, obtains based on state
The sub-optimal velocity artificial potential function controller of related Riccati equation；
The flying speed and posture that the spacecraft is controlled using the sub-optimal velocity artificial potential function controller, make the space flight
Device reaches desired locations and avoiding barrier.
2. spacecraft according to claim 1 intersects barrier-avoiding method automatically, which is characterized in that it is described according to the position to
Amount and desired locations vector building target attract potential function, specifically include:
It is according to the position vector and desired locations vector building target attraction potential functionIts
Middle φaAttract potential function for target；R is the position vector of spacecraft；rfFor the desired locations vector of spacecraft；P is positive semidefinite square
Battle array.
3. spacecraft according to claim 1 intersects barrier-avoiding method automatically, which is characterized in that described to be based on sigmoid letter
Number building Obstacle avoidance potential function, specifically includes:
Obtain the general type of the potential field function of the sigmoid functionWherein γ is barrier
Coverage, N are the surface number of barrier, SiFor the mathematic(al) representation in i-th of face of barrier；
Obtain relative position expression formula S (r, the r of the spacecraft Yu the barrier mass centero)=1- (r-ro)TMo(r-ro)；Its
Middle S (r, ro) be spacecraft and barrier mass center relative position；R is the position vector of spacecraft；roIndicate barrier mass center；
MoFor the information matrix of barrier；
According to describedWith relative position expression formula S (r, the ro)=1- (r-ro)TMo(r-ro) building institute
State Obstacle avoidance potential function
Wherein φrObstacle avoidance potential function for spacecraft relative to barrier；Most short Euler of the d between spacecraft and barrier
Distance；dctFor the distance of spacecraft centroid to desired locations；dotFor the distance of barrier mass center to desired locations；dsIt is the smallest
Stop distance.
4. spacecraft according to claim 1 intersects barrier-avoiding method automatically, which is characterized in that described to be inhaled according to the target
Draw potential function and the Obstacle avoidance potential function determine overall potential function, specifically includes:
Potential function and the Obstacle avoidance potential function is attracted to determine the overall potential function according to the target
Wherein φ is overall potential function；kaFor gravitational potential energy coefficient；krFor repulsion potential energy coefficient, φaAttract potential function for target；For
Obstacle avoidance potential function caused by i-th of barrier, m are the barrier number around spacecraft.
5. spacecraft according to claim 1 intersects barrier-avoiding method automatically, which is characterized in that described according to total body posture
Function determines the control law based on speed artificial potential function, specifically includes:
Determine that liapunov function is according to the overall potential functionWherein V is Li Yapunuo
Husband's function；Gradient for overall potential function φ about Space Vehicle position vector r；For the speed of spacecraft；
First derivative is asked to the liapunov function, is obtainedWhereinFor Li Yapu
The first derivative of promise husband's function；H (φ) is the Hessian matrix of overall potential function φ；For the acceleration of spacecraft；
Ensure describedIt is negative, obtaining the control law based on speed artificial potential function is
Wherein uVAPFFor the control based on speed artificial potential function
Rule；K is positive definite matrix；For the output valve of Space Vehicle System output equation.
6. spacecraft according to claim 1 intersects barrier-avoiding method automatically, which is characterized in that described according to the control law
Attract potential function to carry out the optimization of state correlation Riccati equation the target, obtains time based on state correlation Riccati equation
Excellent speed artificial potential function controller, specifically includes:
Ideal control law u is obtained according to correlated condition Riccati equation*(X)=- R (X)-1B(X)TE(X)X(t)；WhereinR and E is coefficient matrix；Wherein 03×3For 3 × 30 matrixes of dimension, I3×3For 3 × 3 dimension unit squares
Battle array；
According to the ideal control law u*(X)=- R (X)-1B(X)TE (X) X (t) determines the Li Kati shape of spacecraft dynamics equation
FormulaWhereinFor the first derivative of X (t)；For space flight
The optimal velocity of device；For the optimal acceleration of spacecraft；KSDRE(X)=R (X)-1B(X)TE(X)；
For coefficient matrix, wherein 03×3For 3 × 30 matrixes of dimension, I3×3For 3 × 3 dimension unit matrixs, A22For matrix
WhereinFor the track angular speed of spacecraft；Wherein
For the track angle angular speed of spacecraft；rcFor the orbit altitude of main spacecraft；μ is terrestrial gravitation constant；X, y and z is respectively that r exists
Projection in three reference axis, i.e. r=[x, y, z]；rt=[(rc+x)2+y2+z2]12；
The Li Kati form of the spacecraft dynamics equation is subjected to abbreviation, obtains the optimal velocity of spacecraftMost
Excellent accelerationWherein
Determine that target attracts the regulated quantity of potential function according to the optimal velocity and the optimal accelerationWhereinFor regulated quantity；N is coefficient matrix；For expectation
Position rfDerivative；KMFor normal number；P is positive semidefinite matrix；
According to the regulated quantityIt adjusts the target and attracts potential function, to change the control law uVAPF, obtain described be based on
The sub-optimal velocity artificial potential function controller of state correlation Riccati equation.
7. a kind of spacecraft intersects obstacle avoidance system automatically, which is characterized in that the system comprises:
Space Vehicle position vector obtains module, for obtaining the position vector and desired locations vector of spacecraft；
Target attracts potential function to construct module, for constructing target attraction potential letter according to the position vector and desired locations vector
Number；
Obstacle avoidance potential function constructs module, for constructing Obstacle avoidance potential function based on sigmoid function；
Overall potential function determining module, it is total for attracting potential function and the Obstacle avoidance potential function to determine according to the target
Body posture function；
Control law determining module, for determining the control law based on speed artificial potential function according to the overall potential function；
State correlation Riccati equation optimization module, for attracting potential function to carry out state the target according to the control law
Related Riccati equation optimization, obtains the sub-optimal velocity artificial potential function controller based on state correlation Riccati equation；
Spacecraft intersects obstacle avoidance module automatically, for controlling the spacecraft using the sub-optimal velocity artificial potential function controller
Flying speed and posture, so that the spacecraft is reached desired locations and avoiding barrier.
8. spacecraft according to claim 7 intersects obstacle avoidance system automatically, which is characterized in that the target attracts potential function
Building module specifically includes:
Target attracts potential function construction unit, for constructing target attraction potential letter according to the position vector and desired locations vector
Number isWherein φaAttract potential function for target；R is the position vector of spacecraft；rfFor space flight
The desired locations vector of device；P is positive semidefinite matrix.
9. spacecraft according to claim 7 intersects obstacle avoidance system automatically, which is characterized in that the Obstacle avoidance gesture letter
Number building module specifically includes:
Sigmoid function acquiring unit, the general type of the potential field function for obtaining the sigmoid functionWherein γ is the coverage of barrier, and N is the surface number of barrier, SiFor i-th of face of barrier
Mathematic(al) representation；
Relative position expression formula acquiring unit, for obtaining the relative position expression formula of the spacecraft Yu the barrier mass center
S(r,ro)=1- (r-ro)TMo(r-ro)；Wherein S (r, ro) be spacecraft and barrier mass center relative position；R is spacecraft
Position vector；roIndicate barrier mass center；MoFor the information matrix of barrier；
Obstacle avoidance potential function construction unit, for according toWith the phase
To L-expression S (r, ro)=1- (r-ro)TMo(r-ro) the building Obstacle avoidance potential functionWherein φrIt is opposite for spacecraft
In the Obstacle avoidance potential function of barrier；Most short Euler distance of the d between spacecraft and barrier；dctFor spacecraft centroid
To the distance of desired locations；dotFor the distance of barrier mass center to desired locations；dsFor the smallest stop distance.
10. spacecraft according to claim 7 intersects obstacle avoidance system automatically, which is characterized in that the totality potential function is true
Cover half block specifically includes:
Overall potential function determination unit, for attracting potential function and the Obstacle avoidance potential function to determine institute according to the target
State overall potential functionWherein φ is overall potential function；kaFor gravitational potential energy coefficient；krFor repulsion gesture
Energy coefficient, φaAttract potential function for target；For Obstacle avoidance potential function caused by i-th of barrier, m is spacecraft week
The barrier number enclosed.
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