CN108628345A - A kind of electromagnetism Spacecraft formation hovering cooperative control method and system - Google Patents
A kind of electromagnetism Spacecraft formation hovering cooperative control method and system Download PDFInfo
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Abstract
A kind of electromagnetism Spacecraft formation hovering cooperative control method of present invention offer and system, wherein method include：For any one electromagnetism spacecraft, the electromagnetic force suffered by the electromagnetism spacecraft is calculated, obtains electromagnetic force accounting equation；Using the synperiodic circular orbit of elliptic orbit with reference to spacecraft movement as nominal track, the electromagnetism spacecraft is established with reference to the target dynamics equation of Spacecraft Relative Motion, Robust Control Law is designed using sliding-mode control based on target dynamics equation；The magnetic moment of all electromagnetism spacecrafts is allocated according to electromagnetic force accounting equation and Robust Control Law.This method and the control law of system design so that in electromagnetism spacecraft reference orbit real time information can not be obtained and in the case of by various interference effects, can also realize hovering of the electromagnetism Spacecraft formation in space any position, have good robustness；Distributing rationally for electromagnetism magnetic moment of spacecraft is realized using the method for optimization, is conducive to electromagnetism spacecraft orbit and attitude decoupling.
Description
Technical field
The present invention relates to fields of communication technology, more particularly, to a kind of electromagnetism Spacecraft formation hovering Collaborative Control side
Method and system.
Background technology
The adjoint spacecrafts of more for hovering and referring to be in gravitational field are formed into columns under the action of control force, it is opposite to refer to space flight
Device or other natural celestial bodies keep opposing stationary state.Formation hovering technology is in spacecraft in-orbit service, survey of deep space, space flight
Device traces and monitors equal fields and has a wide range of applications.When short distance is hovered, traditional thruster based on impulse principle can be made
At plume contamination and its restricted lifetime, certain tasks even igniting of the stringent limited target of meeting and hovering spacecraft line direction.
In addition, in forming into columns member's spacecraft hovering track non-Kepler's property, inevitable requirement thruster works long hours.Therefore electricity is utilized
Magnetic interaction realizes that the relative orbit control between spacecraft receives the concern of numerous scholars.Electromagnetism spacecraft passes through change
The electric current for the three orthogonal electromagnetic coils installed thereon changes the electromagnetic force that spacecraft is subject to, and then realizes the phase of Spacecraft formation
To orbits controlling, the realization for Spacecraft formation control provides a kind of new approaches.
Introduce after electromagnetic action preferably resolve traditional thruster there are the problem of, but intrinsic non-of electromagnetic action
Linearly, the uncertain noises of reciprocity and space environment determine the control of electromagnetism Spacecraft formation with strong nonlinearity, strong coupling
Conjunction property and uncertain feature, more stringent requirements are proposed for this design to controller.
There are some achievements in research, Ahsun etc. to be based on circle and refer to rail both at home and abroad about the control of electromagnetism Spacecraft formation
The Formation keeping of artificial potential function method and nonlinear autoregressive technique study electromagnetism Spacecraft formation has been respectively adopted in road
Problem, and propose the magnetic moment method for solving by adding constraint or optimization distribution.Kwon etc. uses ground experimental verification to utilize
Superconducting coil generates electromagnetic force and then the feasibility of progress track tracking between star.Abbott etc. is assuming that known to control acceleration
Under the conditions of, a kind of semi-analytic method for solving magnetic moment is given based on sequential quadratic programming algorithm.In addition, domestic scholars also carry out
Numerous studies.Hu Min etc. is based on the accurate relative motion model of double spacecrafts, it is proposed that a kind of Nonlinear Feedback Control Method.Slowly
Increase text etc. to keep devising adaptive control laws for double star electromagnetism spacecraft configuation, and gives the double star based on balancing energy
The analytical expression of magnetic moment distribution.Shao Longfei etc. is studies have shown that the formation control of more electromagnetism spacecrafts can be converted into stage by stage
Double electromagnetism Spacecraft Controls.
Existing achievement in research can solve the Formation keeping and relative orbit of electromagnetism Spacecraft formation to a certain extent
Attitude Tracking and problem, but it is less in studying consider that the inside of kinetic model is uncertain, and this is not in actual task
Certainty is inevitable.Furthermore the control law designed in existing achievement in research is required to the real-time accurate information of reference orbit,
This is very difficult in some cases or even can not be obtainable.In addition, existing achievement in research does not consider to form into columns mostly
Communication between member's spacecraft has not been able to the relative status information for effectively utilizing member's spacecraft, leads to the collaboration formed into columns
Ability is poor and generates the control of redundancy.
Invention content
The present invention causes to overcome the control law designed in the prior art to be required to the real-time accurate information of reference orbit
It is difficult to realize, and the prior art does not consider the communication between formation member spacecraft, has not been able to effectively utilize member's space flight
The relative status information of device causes the cooperative ability formed into columns poor and leads to the problem of the control of redundancy, provides a kind of electromagnetism
Spacecraft formation hovering cooperative control method and system.
On the one hand, the present invention provides a kind of electromagnetism Spacecraft formation hovering cooperative control method, including：
For any one electromagnetism spacecraft, the electromagnetic field that the electromagnetic coil installed on the electromagnetism spacecraft generates is regarded as
Dipole establishes electromagnetic force far field model, calculates the electromagnetic force between each two electromagnetic coil in the model of the electromagnetic force far field,
The first electromagnetic force accounting equation is obtained, and the electricity suffered by the electromagnetism spacecraft is calculated according to the first electromagnetic force accounting equation
Magnetic force obtains the second electromagnetic force accounting equation；
Reference frame is established as coordinate origin using with reference to the barycenter of spacecraft, by described with reference to the ellipse of spacecraft movement
The synperiodic circular orbit of circular orbit establishes the electromagnetism under the reference frame as nominal track based on the nominal track
Spacecraft and the target dynamics equation with reference to Spacecraft Relative Motion use sliding formwork based on the target dynamics equation
Design of control method Robust Control Law；
According to the second electromagnetic force accounting equation and the Robust Control Law to the magnetic moment of all electromagnetism spacecrafts
It is allocated.
Preferably, described that the electromagnetism spacecraft and the ginseng are established based on the nominal track under the reference frame
The target dynamics equation of Spacecraft Relative Motion is examined, specially：
Under the reference frame, the electromagnetism spacecraft and the candidate power with reference to Spacecraft Relative Motion are established
Learn equation；
By the elliptic orbit relative to the deviation of the nominal track, Earth nonspherical gravitation perturbation, solar light pressure, electricity
The gravitation of magnetic force far field model error and other celestial bodies is as Uncertainty, according to the Uncertainty by the candidate power
It learns equation and is converted to the target dynamics equation.
Preferably, described that Robust Control Law is designed using sliding-mode control based on the target dynamics equation, specifically
For：
Sliding surface is obtained according to the current state of the electromagnetism spacecraft and nominal state；
Hitting control law and reaching condition are chosen, based on the sliding surface according to the Hitting control law and the arrival item
Part designs the Robust Control Law.
Preferably, described that Robust Control Law is designed using sliding-mode control based on the target dynamics equation, later
Further include：
It is corresponding that the electromagnetism spacecraft is obtained according to the correspondence between the electromagnetism spacecraft and other electromagnetism spacecrafts
Item is cooperateed with, the collaboration item is added to the Robust Control Law, obtains coordination control laws.
Preferably, the correspondence according to the electromagnetism spacecraft between other electromagnetism spacecrafts obtains collaboration item,
Specially：
Using each electromagnetism spacecraft as node, using the correspondence between each two electromagnetism spacecraft as side, and will
Communication performance between each two electromagnetism spacecraft establishes weighted undirected graph as adjacency matrix；
The corresponding collaboration item of the electromagnetism spacecraft is obtained according to the weighted undirected graph.
Preferably, described to be navigated to all electromagnetism according to the second electromagnetic force accounting equation and the Robust Control Law
The magnetic moment of its device is allocated, specially：
For any one electromagnetism spacecraft, the Robust Control Law is substituted into the second electromagnetic force accounting equation and is obtained
The corresponding constraint equation of electromagnetism spacecraft；
One external force is set, and the external force, which is increased to an electromagnetism spacecraft in all electromagnetism spacecrafts, to be corresponded to
Constraint equation in；
Object function is set based on energetic optimum and the principle of magnetic moment configuration equilibrium and track profile decoupling, according to all
The corresponding constraint equation of electromagnetism spacecraft and the object function are allocated the magnetic moment of all electromagnetism spacecrafts.
Preferably, the object function is specially：
Wherein, uiIndicate the electromagnetic force that i spacecrafts are subject to；W1i、W2iIndicate weight coefficient matrix；τiIndicate i space flight
The electromagnetic interference torque that device is subject to；γiIt is the balancing coefficient of selection；f0Indicate external force；WoIt is its balancing coefficient matrix；N indicates institute
There is the total quantity of spacecraft.
On the one hand, the present invention provides a kind of electromagnetism Spacecraft formation hovering cooperative control system, including：
Electromagnetic force computing module is used for for any one electromagnetism spacecraft, the electromagnetism that will be installed on the electromagnetism spacecraft
The electromagnetic field that coil generates is regarded as dipole, establishes electromagnetic force far field model, calculates each two in the model of the electromagnetic force far field
Electromagnetic force between electromagnetic coil obtains the first electromagnetic force accounting equation, and is calculated according to the first electromagnetic force accounting equation
Electromagnetic force suffered by the electromagnetism spacecraft obtains the second electromagnetic force accounting equation；
Design of control law module, for the barycenter for referring to spacecraft to be established reference frame as coordinate origin, by institute
The synperiodic circular orbit of elliptic orbit with reference to spacecraft movement is stated as nominal track, institute is based under the reference frame
It states nominal track and establishes the electromagnetism spacecraft and the target dynamics equation with reference to Spacecraft Relative Motion, be based on the mesh
It marks kinetics equation and Robust Control Law is designed using sliding-mode control；
Magnetic moment distribution module is used for according to the second electromagnetic force accounting equation and the Robust Control Law to all described
The magnetic moment of electromagnetism spacecraft is allocated.
On the one hand, the present invention provides a kind of equipment of electromagnetism Spacecraft formation hovering cooperative control method, including：
At least one processor；And
At least one processor being connect with the processor communication, wherein：
The memory is stored with the program instruction that can be executed by the processor, and the processor calls described program to refer to
It enables and is able to carry out any of the above-described method.
On the one hand, the present invention provides a kind of non-transient computer readable storage medium, which is characterized in that the non-transient meter
Calculation machine readable storage medium storing program for executing stores computer instruction, and the computer instruction makes the computer execute any of the above-described side
Method.
A kind of electromagnetism Spacecraft formation hovering cooperative control method provided by the invention and system, for any one electromagnetism
The electromagnetic field that the electromagnetic coil installed on the electromagnetism spacecraft generates is regarded as dipole, establishes electromagnetic force far field mode by spacecraft
Type calculates the electromagnetic force between each two electromagnetic coil in the model of electromagnetic force far field, obtains the first electromagnetic force accounting equation, and root
The electromagnetic force suffered by the electromagnetism spacecraft is calculated according to the first electromagnetic force accounting equation, obtains the second electromagnetic force accounting equation；It will
Reference frame is established as coordinate origin with reference to the barycenter of spacecraft, the elliptic orbit with reference to spacecraft movement is synperiodic
Circular orbit is established the electromagnetism spacecraft with reference to the target dynamics equation of Spacecraft Relative Motion, is based on as nominal track
Target dynamics equation designs Robust Control Law using sliding-mode control；According to the second electromagnetic force accounting equation and robust control
Rule is allocated the magnetic moment of all electromagnetism spacecrafts.This method and system are set for the hovering of electromagnetism Spacecraft formation system track
Count a kind of robust Collaborative Control so that reference orbit real time information can not be obtained in electromagnetism spacecraft and by various interference effects
In the case of, it can also realize hovering of the electromagnetism Spacecraft formation in space any position, there is good robustness.And herein
On the basis of control, distributing rationally for electromagnetism Spacecraft formation magnetic moment is realized using the method for optimization, is obtained by this optimization
Magnetic moment be beneficial to electromagnetism spacecraft orbit and attitude decoupling.
Description of the drawings
Fig. 1 is a kind of overall flow signal of electromagnetism Spacecraft formation hovering cooperative control method of the embodiment of the present invention
Figure；
Fig. 2 is the schematic diagram of the spaceborne two electromagnetic coils interaction of electromagnetism of the embodiment of the present invention；
Fig. 3 be the embodiment of the present invention electromagnetic force far field model in magnetic dipolar interaction schematic diagram；
Fig. 4 is according to electromagnetism Spacecraft formation hovering configuration schematic diagram in the emulation experiment of the embodiment of the present invention；
Fig. 5 is a kind of overall structure signal of electromagnetism Spacecraft formation hovering cooperative control system of the embodiment of the present invention
Figure；
Fig. 6 is a kind of structural framing of the equipment of electromagnetism Spacecraft formation hovering cooperative control method of the embodiment of the present invention
Schematic diagram.
Specific implementation mode
With reference to the accompanying drawings and examples, the specific implementation mode of the present invention is described in further detail.Implement below
Example is not limited to the scope of the present invention for illustrating the present invention.
Effect of the adjoint spacecrafts of refer to be in gravitational field more in control force it should be noted that formation is hovered
Under, it is opposite to keep opposing stationary state with reference to spacecraft or other natural celestial bodies.The present invention chooses electromagnetism spacecraft as companion
With spacecraft, i.e., electromagnetism spacecraft, that is, acute pyogenic infection of finger tip in the present invention is with spacecraft.On this basis, the present invention is directed to electromagnetism space flight
The hovering of device fleet system track designs a kind of robust Collaborative Control so that can not obtain reference orbit in member's spacecraft and believe in real time
Cease and by various interference effects in the case of, realize electromagnetism Spacecraft formation space any position hovering.And it controls herein
On the basis of system, balanced index is most saved and consumed based on energy, and electromagnetism Spacecraft formation magnetic moment is realized using the method for optimization
Distribute rationally.The specific implementation process is as follows：
Fig. 1 is a kind of overall flow signal of electromagnetism Spacecraft formation hovering cooperative control method of the embodiment of the present invention
Figure, as shown in Figure 1, the present invention provides a kind of electromagnetism Spacecraft formation hovering cooperative control method, including：
S1, for any one electromagnetism spacecraft, the electromagnetic field that the electromagnetic coil installed on the electromagnetism spacecraft is generated
It is regarded as dipole, establishes electromagnetic force far field model, calculates the electromagnetic force between each two electromagnetic coil in the model of electromagnetic force far field,
The first electromagnetic force accounting equation is obtained, and the electromagnetism suffered by the electromagnetism spacecraft is calculated according to the first electromagnetic force accounting equation
Power obtains the second electromagnetic force accounting equation；
Specifically, each electromagnetism spacecraft is installed above there are three orthogonal electromagnetic coil, and coil will produce phase after being powered
The electromagnetic force and electromagnetic torque of interaction can realize the orbit maneuver and posture tune of electromagnetism spacecraft using the power and torque
It is whole.The distance between interaction between electromagnetic coil and hub of a spool and the space direction of coil are related.Using Biot-Sa
Electromagnetic force and electromagnetic torque between two hot-wire coils can be accurately calculated by cutting down your law.It is located at as shown in Fig. 2, setting coil 2
In the electromagnetic field of coil 1, on coil 2 electric current infinitesimal is integrated in the electromagnetic field of coil 1, you can acquire coil 2 by
To coil 1 to its electromagnetic force F2With torque T2, while F2And T2Electromagnetic force and electromagnetism as between coil 1 and coil 2
Torque, specific solution formula such as following formula (1), (2)：
Wherein, μ0For space permeability, and μ0=4 π × 10-7N×A-2；i1And i2It indicates on coil 1 and coil 2 respectively
Electrical current；a1And a2The radius of coil 1 and coil 2 is indicated respectively；dl1And dl2Indicate that the length of coil 1 and coil 2 is micro- respectively
Member；D indicates the distance between the length infinitesimal of two coils.
The accurate electromagnetic force formula form acquired by above-mentioned integral is complicated, is not easy directly to apply in engineering.Research hair
It is existing, when the distance between two coils are more than 8 times of coil diameter, by the electromagnetic field that coil generates be regarded as dipole obtain it is remote
Field electromagnetic force model also disclosure satisfy that the accuracy requirement in engineering.In view of this, in the present embodiment, navigate for any one electromagnetism
The electromagnetic field that the electromagnetic coil installed on the electromagnetism spacecraft generates is regarded as dipole, establishes electromagnetic force far field model by its device,
As shown in figure 3, in the model of electromagnetic force far field, coil electromagnetism field is considered as dipole, size and Orientation is described with magnetic moment, magnetic
The solution formula of square u is such as following formula (3)：
μ=NISn (3)
Wherein N is the number of turns of coil, and I is current value, and S is the area of coil, n be current-carrying plane normal direction unit to
Amount obeys the right-hand rule.
Under the model of electromagnetic force far field, the electromagnetic force F between two coils2With electromagnetic torque T2Can use respectively following (4),
(5) formula is calculated：
Wherein, μ0For space permeability；u1And u2The magnetic moment of coil 1 and coil 2 is indicated respectively；R indicates two hub of a spools
The distance between；Above formula (4) is the first electromagnetic force accounting equation.It can be calculated according to the first electromagnetic force accounting equation as a result,
The electromagnetic force that each electromagnetic coil is subject in the spacecraft.On this basis, three electromagnetic coils on the spacecraft are subject to
Electromagnetic force carries out summation and can be obtained the electromagnetic force that the electromagnetism spacecraft is integrally subject to.Assuming that fleet system has N number of electromagnetism space flight
Device, number i=1,2,3 ..., N, electromagnetism spacecraft can generate the magnetic moment of arbitrary direction.The electromagnetism boat for being i for number
Its device, the electromagnetic force being subject to can then be acquired by the second electromagnetic force accounting equation, wherein the second electromagnetic force accounting equation is specific
Such as following formula (6)：
Wherein, FiIndicate to number the spacecraft for being i by the resultant force of electromagnetic force, FijIndicate j spacecrafts to i spacecrafts
Electromagnetic action, μi、μjThe magnetic moment of i spacecrafts and j spacecrafts, r are indicated respectivelyijIndicate that i spacecrafts navigate relative to No. j
I spacecrafts are directed toward in the position of its device from j spacecrafts.
S2 establishes reference frame using with reference to the barycenter of spacecraft as coordinate origin, will be with reference to the ellipse of spacecraft movement
The synperiodic circular orbit of circular orbit as nominal track, under reference frame based on nominal track establish the electromagnetism spacecraft with
With reference to the target dynamics equation of Spacecraft Relative Motion, robust is designed using sliding-mode control based on target dynamics equation
Control law；
Specifically, the relative motion between description electromagnetism spacecraft, is firstly introduced into geocentric inertial coordinate system, Earth central inertial
Coordinate system coordinate origin is located at earth center, and X-axis is located at equatorial plane, is directed toward first point of Aries direction, and Z axis is flat perpendicular to equator
Face, it is that just, Y-axis constitutes right-handed system with X-axis, Z axis to be directed toward the arctic.On this basis, using the barycenter with reference to spacecraft as coordinate
Origin establishes reference frame, and it is just that y-axis is in orbit plane that x-axis, which is radially directed toward from earth center with reference to spacecraft centroid,
Interior vertical with x-axis, it is that just, z-axis constitutes right-handed coordinate system with x-axis, y-axis to be directed toward satellite direction of advance.
On the basis of the above, if it is remote not small to applying the distance between electromagnetism spacecraft in control and formation with reference to spacecraft
In the distance with reference to spacecraft centroid to the earth's core, then under above-mentioned reference frame, electromagnetism spacecraft during hovering is formed into columns can be established
With the kinetics equation with reference to Spacecraft Relative Motion.However, running parameter in above-mentioned kinetics equation with reference to space flight
Reference orbit residing for device is related, if according to above-mentioned kinetics equation design control law, needs to obtain the real-time of reference orbit
Accurate information, however this is very difficult in some cases or even can not possibly obtain.
In view of this, in the present embodiment, by the synperiodic round rail of elliptic orbit (reference orbit) with reference to spacecraft movement
Road is as nominal track, and on this basis, elliptic orbit is interfered relative to the deviation of nominal circular orbit, perturbation of earths gravitational field
And air drag etc. is individually sorted out, and is handled as uncertain factor.Above-mentioned kinetics equation is converted into target as a result,
Kinetics equation.
On the basis of the above, the target dynamics equation based on above-mentioned acquisition designs robust control using sliding-mode control
Rule.The formation hovering of electromagnetism spacecraft can be realized according to the Robust Control Law.The principle of sliding formwork control is according to system institute's phase
The dynamic characteristic of prestige carrys out the tangential-hoop method of design system, makes extroversion of the system mode from hyperplane by sliding mode control
Tangential-hoop method collects.System once reaches tangential-hoop method, and control action will ensure that system reaches system along tangential-hoop method
Origin, this process slided to origin along tangential-hoop method are known as sliding formwork control.Since the characteristic and parameter of system only depend on
It is not related with external interference in the tangential-hoop method of design, so Sliding mode variable structure control has very strong robustness.
S3 is allocated the magnetic moment of all electromagnetism spacecrafts according to the second electromagnetic force accounting equation and Robust Control Law.
Specifically, by above-mentioned second electromagnetic force accounting equation it is found that the second electromagnetic force accounting equation can indicate that electromagnetism navigates
Relationship between the electromagnetic force that its device is subject to and magnetic moment.In order to realize that the formation of electromagnetism spacecraft is hovered, suffered by electromagnetism spacecraft
The electromagnetic force arrived should be consistent with the Robust Control Law of above-mentioned acquisition.Therefore, it is above-mentioned obtain Robust Control Law on the basis of, will
After Robust Control Law substitutes into the second electromagnetic force equation, the corresponding magnetic of each electromagnetism spacecraft can be calculated by optimization method
Square.In the present embodiment, in above-mentioned optimization method other than considering that energy expenditure is optimal and balanced, it is also contemplated that electromagnetic coil
The torque and the external force needed for maneuverable spacecraft formation barycenter of generation.The magnetic moment point of all electromagnetism spacecrafts can be realized as a result,
Match.
A kind of electromagnetism Spacecraft formation hovering cooperative control method provided by the invention, for any one electromagnetism space flight
The electromagnetic field that the electromagnetic coil installed on the electromagnetism spacecraft generates is regarded as dipole, establishes electromagnetic force far field model, counted by device
The electromagnetic force between each two electromagnetic coil in the model of electromagnetic force far field is calculated, obtains the first electromagnetic force accounting equation, and according to the
One electromagnetic force accounting equation calculates the electromagnetic force suffered by the electromagnetism spacecraft, obtains the second electromagnetic force accounting equation；It will refer to
The barycenter of spacecraft establishes reference frame as coordinate origin, by the synperiodic round rail of elliptic orbit with reference to spacecraft movement
Road establishes the electromagnetism spacecraft with reference to the target dynamics equation of Spacecraft Relative Motion, is based on target as nominal track
Kinetics equation designs Robust Control Law using sliding-mode control；According to the second electromagnetic force accounting equation and Robust Control Law pair
The magnetic moment of all electromagnetism spacecrafts is allocated.This method designs a kind of robust for the hovering of electromagnetism Spacecraft formation system track
Collaborative Control so that it can not obtain reference orbit real time information in electromagnetism spacecraft and in the case of by various interference effects,
Also it can realize hovering of the electromagnetism Spacecraft formation in space any position, there is good robustness.And the base controlled herein
On plinth, distributing rationally for electromagnetism Spacecraft formation magnetic moment is realized using the method for optimization, it will by this obtained magnetic moment that optimizes
Be conducive to electromagnetism spacecraft orbit and attitude decoupling.
Based on any of the above-described embodiment, a kind of electromagnetism Spacecraft formation hovering cooperative control method is provided, in reference coordinate
The target dynamics equation of the electromagnetism spacecraft and reference Spacecraft Relative Motion is established under system based on nominal track, specially：
Under reference frame, the candidate kinetics equation of the electromagnetism spacecraft and reference Spacecraft Relative Motion is established；By oval rail
Road relative to the deviation of nominal track, Earth nonspherical gravitation perturbation, solar light pressure, electromagnetic force far field model error and other
Candidate kinetics equation is converted to target dynamics equation by the gravitation of celestial body as Uncertainty, according to Uncertainty.
Specifically, after establishing reference frame as coordinate origin using the barycenter with reference to spacecraft, it is assumed that not to ginseng
It examines the distance between electromagnetism spacecraft during spacecraft applies control and forms into columns and is much smaller than the distance with reference to spacecraft centroid to the earth's core,
Then under reference frame, the candidate kinetics equation of electromagnetism spacecraft and reference Spacecraft Relative Motion in hovering formation
For：
Wherein subscript i=1,2,3 ..., N indicate the number of spacecraft in hovering formation, ρi=[xi yi zi]TIndicate hovering
Positions of the spacecraft i in orbital coordinate system.umhiIndicate the electromagnetic force that hovering spacecraft i is subject to, udhiIndicate hovering spacecraft i
It is taken the photograph caused by the external perturbation being subject to, including electromagnetism force modeling inaccuracy, aerodynamic force, solar light pressure and other celestial body gravitations
It is dynamic, udoIndicate that the external perturbation being subject to reference to spacecraft, including aerodynamic force, solar radiation pressure perturbation and other celestial body gravitations cause
's.Coefficient matrix D in above formulaeAnd KeRespectively：
Wherein, R indicate with reference to spacecraft centroid to the earth's core distance, ω,The track angle speed with reference to spacecraft is indicated respectively
Degree and angular acceleration.
Above-mentioned candidate's kinetics equation is the differential equation of a coefficient time-varying, the parameter changed in formula all with reference to space flight
The elliptic orbit (reference orbit) of device movement is related, if will need to obtain according to candidate kinetics equation design control law refers to rail
The real-time accurate information in road, however this is difficult to accomplish in some cases.In view of this, in the present embodiment by one with it is ellipse
The synperiodic circular orbit of circular orbit as nominal track, by elliptic orbit relative to the deviation of nominal track, the earth is aspherical draws
Power perturbation, solar light pressure, electromagnetic force far field model error and other celestial bodies gravitation as Uncertainty.It as a result, will not be really
It is quantitative to substitute into candidate kinetics equation, then target dynamics equation is can get, specially：
Wherein udi=udhi-udo, indicate that the opposite outside with reference to Spacecraft Relative Motion model of hovering spacecraft is uncertain
Amount；Δ D includes perturbation of the elliptic orbit relative to the deviation and kinetics equation parameter of nominal track, and Δ K includes oval rail
Perturbation caused by the aspherical gravitation of deviation and the earth of the road relative to nominal track and the perturbation of kinetics equation parameter.Due to
It is elliptical semi-major axis with the radius of the synperiodic circular orbit of elliptic orbit, therefore matrix D in above formulac、KcValue be respectively：
Meanwhile the upper bound of uncertain matrix is represented by：
|udi|≤f (x, t), f (x, t) >=0
Wherein, αiAnd βjIt is perturbation parameter；EiAnd FjIt is perturbation matrices；F (x, t) indicates the upper of external Uncertainty
Bound function；aiAnd bjRespectively αiAnd βjThe upper bound.
After above-mentioned processing, the control law designed according to target dynamics equation will no longer be required to elliptic boundary value proplem
Real-time precise information, be more conducive to and realized in engineering.In addition, target dynamics equation considers and causes spacecraft
All inside and outside uncertain factors that track deviates, the control law thus designed will have stronger robustness.
A kind of electromagnetism Spacecraft formation hovering cooperative control method provided by the invention, under reference frame, establishing should
The candidate kinetics equation of electromagnetism spacecraft and reference Spacecraft Relative Motion；Deviation by elliptic orbit relative to nominal track
As Uncertainty, candidate kinetics equation is converted to by target dynamics equation according to Uncertainty, it thus can be according to target
Kinetics equation design control law.The target dynamics equation that this method is established, which considers, causes all of spacecraft orbit deviation
Inside and outside uncertain factor, the control law designed according to the target dynamics equation will no longer be required to the real-time of elliptic boundary value proplem
Precise information has stronger robustness.
Based on any of the above-described embodiment, a kind of electromagnetism Spacecraft formation hovering cooperative control method is provided, it is dynamic based on target
Mechanical equation designs Robust Control Law using sliding-mode control, specially：According to the current state and mark of the electromagnetism spacecraft
Title state obtains sliding surface；Hitting control law and reaching condition are chosen, based on sliding surface according to Hitting control law and reaching condition
Design Robust Control Law.
Specifically, on the basis of establishing target dynamics equation, the current state of electromagnetism spacecraft and nominal is obtained
State.By taking electromagnetism spacecraft i as an example, nominal state isIt can be in the hope of the deviation of current state and nominal state
For
Choose sliding surface Si, slide surface function formula specific as follows：
Wherein, Λ=diag { λ r }, λ r>0, r=1,2,3.Be not difficult to find out, the state motion on sliding surface be it is stable,
Next design reaches movement, to above-mentioned sliding surface function derivation, can get following formula：
Since that considers is the formation hovering problem of electromagnetism spacecraft, so have
On this basis, above formula (8) can be reduced to following formula (9)：
On the basis of the above, Hitting control law such as following formula is chosen：
Wherein, HiAnd εiIt is matrix parameter.
In order to eliminate sliding motion shivering on sliding-mode surface, saturation function sat (x) is selected to replace sign function.Function
Sat (x) is specific as follows：
Comparison (9), (10) two formulas obtain equivalent control and are：
There are uncertain parameters in formula (11) control, can not directly use, and to eliminate uncertain parameter, use following formula first
(12) control is replaced.
To determine z1i、z2i, above formula (12) is substituted into above formula (9) and obtains following formula (13).
Choosing reaching condition is：
It is write as component form and obtains following formula：
Wherein, subscript r=1,2,3 indicate r-th of component of vector, vrThe r rows of (*) representing matrix *, if taking
Bring (16), (17) into (15), more every size eliminates indeterminate, may make reaching condition (14) formula full
Foot.
Formula (12), (16), (17) constitute the control law that electromagnetism Spacecraft formation hovers, which has been able to realize electricity
The hovering task of magnetic Spacecraft formation, and there is stronger robustness to uncertain noises.
A kind of electromagnetism Spacecraft formation hovering cooperative control method provided by the invention, according to the current of the electromagnetism spacecraft
State and nominal state obtain sliding surface；Choose Hitting control law and reaching condition, based on sliding surface according to Hitting control law and
Reaching condition designs Robust Control Law.The control law obtained by this method will no longer be required to the real-time accurate of elliptic boundary value proplem
Information has stronger robustness.
Based on any of the above-described embodiment, a kind of electromagnetism Spacecraft formation hovering cooperative control method is provided, it is dynamic based on target
Mechanical equation designs Robust Control Law using sliding-mode control, further includes later：According to the electromagnetism spacecraft and other electromagnetism
Correspondence between spacecraft obtains the corresponding collaboration item of the electromagnetism spacecraft, and collaboration item is added to Robust Control Law, is obtained
Obtain coordination control laws.
Specifically, the Robust Control Law of above-mentioned design only considered form into columns in electromagnetism spacecraft itself position and speed it is inclined
Poor information does not use the status information of other electromagnetism spacecrafts, from fleet system level, designed robust control
Rule is merely able to reach local superperformance, is examined closely from global visual angle, there are the wastes of control.
In view of this, in the present embodiment, Robust Control Law is improved, to be handed over using the information between electromagnetism spacecraft
Change realization global collaborative.Specifically, it is somebody's turn to do according to the correspondence between some electromagnetism spacecraft and other electromagnetism spacecrafts
Collaboration item is added to Robust Control Law, you can obtain coordination control laws by the corresponding collaboration item of electromagnetism spacecraft.The Collaborative Control
Rule can effectively improve the synergisticing performance in fleet system between electromagnetism spacecraft.
A kind of electromagnetism Spacecraft formation hovering cooperative control method provided by the invention, is adopted based on target dynamics equation
After designing Robust Control Law with sliding-mode control, closed according to the communication between the electromagnetism spacecraft and other electromagnetism spacecrafts
System obtains the corresponding collaboration item of the electromagnetism spacecraft, and collaboration item is added to Robust Control Law, obtains coordination control laws.By this
The coordination control laws that method obtains can effectively improve the synergisticing performance in fleet system between electromagnetism spacecraft, advantageously reduce control
System waste.
Based on any of the above-described embodiment, a kind of electromagnetism Spacecraft formation hovering cooperative control method is provided, according to the electromagnetism
Correspondence of the spacecraft between other electromagnetism spacecrafts obtains collaboration item, specially：Using each electromagnetism spacecraft as section
Point, using the correspondence between each two electromagnetism spacecraft as side, and by the communication performance between each two electromagnetism spacecraft
As adjacency matrix, weighted undirected graph is established；The corresponding collaboration item of the electromagnetism spacecraft is obtained according to weighted undirected graph.
Specifically, the relationship in Spacecraft formation between member's spacecraft is described for clarity, and graph theory is incorporated herein
Related notion.One weighted undirected graph G (V, E, A) is by set of node V={ 1,2 ..., N }, side collectionWith weighted adjacent square
Battle array A=a [ij] is formed.Node indicates that the electromagnetism spacecraft in forming into columns, side indicate that the communication in forming into columns between electromagnetism spacecraft is closed
System, adjacency matrix indicate the communication performance of electromagnetism spacecraft in forming into columns.If can be communicated between two spacecraft i, j in non-directed graph,
Then side (j, i) ∈ E and aij=aji>0, otherwise aij=0.It is generally acknowledged that spacecraft is with itself, there is no communication, i.e. aii=0.If
There are paths between any two node in figure, then it is connection to claim the non-directed graph.
On the basis of above-mentioned graph theory, it is contemplated that the communication delay in formation between electromagnetism spacecraft, to above-mentioned robust control
System rule increases by a collaboration item, obtains coordination control laws such as formula：
Wherein, τijIndicate the communication delay between spacecraft i and spacecraft j.
A kind of electromagnetism Spacecraft formation hovering cooperative control method provided by the invention, using each electromagnetism spacecraft as section
Point, using the correspondence between each two electromagnetism spacecraft as side, and by the communication performance between each two electromagnetism spacecraft
As adjacency matrix, weighted undirected graph is established；The corresponding collaboration item of the electromagnetism spacecraft is obtained according to weighted undirected graph, and then will
Collaboration item increases to Robust Control Law and obtains coordination control laws.The collaboration item that this method obtains considers electromagnetism spacecraft in formation
Between communication delay, thus obtained coordination control laws can effectively improve the concertedness between electromagnetism spacecraft in fleet system
Energy.
Based on any of the above-described embodiment, a kind of electromagnetism Spacecraft formation hovering cooperative control method is provided, according to the second electricity
Calculation of magnetic force equation and Robust Control Law are allocated the magnetic moment of all electromagnetism spacecrafts, specially：For any one electricity
Robust Control Law is substituted into the second electromagnetic force accounting equation and obtains the corresponding constraint equation of electromagnetism spacecraft by magnetic spacecraft；If
An external force is set, external force is increased in the corresponding constraint equation of an electromagnetism spacecraft in all electromagnetism spacecrafts；It is based on
Object function is arranged in energetic optimum and the principle of magnetic moment configuration equilibrium and track profile decoupling, according to all electromagnetism spacecrafts pair
The constraint equation and object function answered are allocated the magnetic moment of all electromagnetism spacecrafts.
Specifically, it for any one electromagnetism spacecraft, is calculated obtaining corresponding second electromagnetic force of the electromagnetism spacecraft
After equation and Robust Control Law, in order to reach hovering of forming into columns, which need to be with the electromagnetism
Electromagnetic force equilibrium suffered by spacecraft.It can be obtained in view of this, Robust Control Law is substituted into the second electromagnetic force accounting equation
The corresponding constraint equation of electromagnetism spacecraft.There is only magnetic moment variables in constraint equation as a result, on this basis, can combine
The corresponding constraint equation of all electromagnetism spacecrafts solves the magnetic moment variable in equation, to realize that magnetic moment distributes.
However, the resultant force for the electromagnetic force being subject to due to entire fleet system is zero, it is clear that in only interaction electromagnetic force
In the case of, system barycenter can not change, and cannot achieve the hovering of any position, thus an optional spacecraft in systems,
Apply an external force on the spacecraft, centroid position is changed by the external force.Increase on some constraint equation as a result,
The external force.
On the basis of the above, it is assumed that fleet system has N number of electromagnetism spacecraft, number i=1,2,3 ..., N, number i
The corresponding second electromagnetic force accounting equation formula specific as follows of spacecraft：
Assuming that above-mentioned external force is applied on N spacecrafts, then the corresponding second electromagnetic force accounting equation of N spacecrafts is such as
Under：
Wherein, foExpression is applied to No. N spaceborne external force.
It can be seen that electromagnetism Spacecraft formation system is altogether by independent constraint 3N from analysis above, but phase
Mutual independent variable has 3N+3 (comprising 3N magnetic moment variable and 3 external force variables), therefore system variable has the freedom of redundancy
Degree, the optimization problem that can convert the problem to belt restraining solve.In the present embodiment, to make the magnetic of electromagnetism spacecraft
Square energy expenditure and external force fuel can be more balanced, decoupled based on energetic optimum and magnetic moment configuration equilibrium and track profile
Object function is arranged in principle, and solving all magnetic moments further according to the corresponding constraint equation of all electromagnetism spacecrafts and object function becomes
Amount, you can the magnetic moment of all electromagnetism spacecrafts is allocated.
A kind of electromagnetism Spacecraft formation hovering cooperative control method provided by the invention, for any one electromagnetism space flight
Robust Control Law is substituted into the second electromagnetic force accounting equation and obtains the corresponding constraint equation of electromagnetism spacecraft by device；Setting one
External force increases to external force in the corresponding constraint equation of an electromagnetism spacecraft in all electromagnetism spacecrafts；Most based on energy
Object function is arranged in the principle of excellent and magnetic moment configuration equilibrium and track profile decoupling, corresponding about according to all electromagnetism spacecrafts
Shu Fangcheng and object function are allocated the magnetic moment of all electromagnetism spacecrafts.This method is optimal in addition to considering energy expenditure
Outside equilibrium, it is also contemplated that the external force needed for torque and maneuverable spacecraft formation barycenter that electromagnetic coil generates, by this excellent
Change obtained magnetic moment and is beneficial to electromagnetism spacecraft orbit and attitude decoupling.
Based on any of the above-described embodiment, a kind of electromagnetism Spacecraft formation hovering cooperative control method, object function tool are provided
Body is：
Wherein, uiIndicate the electromagnetic force that i spacecrafts are subject to；W1i、W2iIndicate weight coefficient matrix；τiIndicate i space flight
The electromagnetic interference torque that device is subject to；γiIt is the balancing coefficient of selection；f0Indicate external force；WoIt is its balancing coefficient matrix；N indicates institute
There is the total quantity of spacecraft.
A kind of electromagnetism Spacecraft formation hovering cooperative control method provided by the invention, is configured based on energetic optimum and magnetic moment
The principle of balanced and track profile decoupling is arranged object function, so according to the corresponding constraint equation of all electromagnetism spacecrafts and
Object function is allocated the magnetic moment of all electromagnetism spacecrafts.This method is optimal and balanced in addition to considering energy expenditure
Outside, it is also contemplated that the external force needed for torque and maneuverable spacecraft formation barycenter that electromagnetic coil generates is obtained by this optimization
Magnetic moment be beneficial to electromagnetism spacecraft orbit and attitude decoupling.
To verify the performance for the control law that any of the above-described embodiment designs, the formation of 4 electromagnetism spacecrafts compositions is carried out
Simulation calculation, the formation configuration that Spacecraft formation uses are as shown in Figure 4.Initial time, totally 4 spacecrafts are located at by A, B, C and D
On 4 vertex of the positive tetrahedron of the long 15m of rib, the center of positive tetrahedron is located at reference to spacecraft.Assuming that the position of member's spacecraft
Set a degree of random perturbation being subject to speed.The quality of member's spacecraft is 100kg in formation, and coil radius is
The coil turn of 1m, 4 spacecrafts are 100.The parameter selection of controller is Hi=10-2×I3×3、εI=10-7×I3×3、Λi
=10-2×I3×3.Consider electromagnetic force modeling error, earth J2 perturbations, earth's magnetic field perturbation, other astronomical perturbations and sunlight
Pressure, the upper bound of modus ponens uncertain parameter is respectively ai=10-5、bj=10-7, f=10-7.Consider three spacecraft link cyclization, separately
An outer spacecraft is connected into the Communication topology of the triangular loop, and it is 5s to take spacecraft communication delay.When magnetic moment solves, examine
Consider that energy most saves, external force is minimum needed for the decoupling of balancing energy, electromagnetic force and torque and system, configures magnetic moment parameter value
For:
W1i=10-11×I3×3、W2i=10-9×I3×3、γi=102、Wo=105×I3×3；Then it is imitated with Matlab
Very.
From simulation result as can be seen that in the case of existence position and perturbation of velocity, according to the method provided by the invention
The robust synovial membrane collaborative controller of design can realize the playback of track using electromagnetic interaction in 700s, and position with
Track error is 10-6The order of magnitude, controller is to the tracking error of speed 10-8The order of magnitude has higher precision.Meanwhile optimizing
Magnetic moment quantity allotted grade later is 105, which can be realized with superconducting coil.The electromagnetic force needed is controlled in mN magnitudes.
Simulation result shows that the electromagnetism Spacecraft formation robust collaborative controller that the present invention designs can effectively realize that Spacecraft formation is appointed
The hovering task of meaning position, to inside and outside uncertain with stronger robustness existing for system.
Fig. 5 is a kind of overall structure signal of electromagnetism Spacecraft formation hovering cooperative control system of the embodiment of the present invention
Figure provides a kind of electromagnetism Spacecraft formation hovering cooperative control system as shown in figure 5, being based on any of the above-described embodiment, including：
Electromagnetic force computing module 1 is used for for any one electromagnetism spacecraft, the electromagnetism that will be installed on the electromagnetism spacecraft
The electromagnetic field that coil generates is regarded as dipole, establishes electromagnetic force far field model, calculates each two electromagnetism in the model of electromagnetic force far field
Electromagnetic force between coil obtains the first electromagnetic force accounting equation, and calculates electromagnetism boat according to the first electromagnetic force accounting equation
Electromagnetic force suffered by its device obtains the second electromagnetic force accounting equation；
Design of control law module 2 will join for the barycenter for referring to spacecraft to be established reference frame as coordinate origin
The synperiodic circular orbit of elliptic orbit of spacecraft movement is examined as nominal track, is built based on nominal track under reference frame
The electromagnetism spacecraft is found with reference to the target dynamics equation of Spacecraft Relative Motion, sliding formwork is used based on target dynamics equation
Design of control method Robust Control Law；
Magnetic moment distribution module 3 is used for according to the second electromagnetic force accounting equation and Robust Control Law to all electromagnetism spacecrafts
Magnetic moment be allocated.
Specifically, the present invention provides a kind of electromagnetism Spacecraft formation hovering cooperative control system, including electromagnetic force calculates mould
Block 1, design of control law module 2 and magnetic moment distribution module 3 are realized by the cooperation of each module in any of the above-described embodiment of the method
Method, specific implementation process can refer to above method embodiment, and details are not described herein again.
A kind of electromagnetism Spacecraft formation hovering cooperative control system provided by the invention, for any one electromagnetism space flight
The electromagnetic field that the electromagnetic coil installed on the electromagnetism spacecraft generates is regarded as dipole, establishes electromagnetic force far field model, counted by device
The electromagnetic force between each two electromagnetic coil in the model of electromagnetic force far field is calculated, obtains the first electromagnetic force accounting equation, and according to the
One electromagnetic force accounting equation calculates the electromagnetic force suffered by the electromagnetism spacecraft, obtains the second electromagnetic force accounting equation；It will refer to
The barycenter of spacecraft establishes reference frame as coordinate origin, by the synperiodic round rail of elliptic orbit with reference to spacecraft movement
Road establishes the electromagnetism spacecraft with reference to the target dynamics equation of Spacecraft Relative Motion, is based on target as nominal track
Kinetics equation designs Robust Control Law using sliding-mode control；According to the second electromagnetic force accounting equation and Robust Control Law pair
The magnetic moment of all electromagnetism spacecrafts is allocated.The system designs a kind of robust for the hovering of electromagnetism Spacecraft formation system track
Collaborative Control so that it can not obtain reference orbit real time information in electromagnetism spacecraft and in the case of by various interference effects,
Also it can realize hovering of the electromagnetism Spacecraft formation in space any position, there is good robustness.And the base controlled herein
On plinth, distributing rationally for electromagnetism Spacecraft formation magnetic moment is realized using the method for optimization, it will by this obtained magnetic moment that optimizes
Be conducive to electromagnetism spacecraft orbit and attitude decoupling.
Fig. 6 shows a kind of structural frames of the equipment of electromagnetism Spacecraft formation hovering cooperative control method of the embodiment of the present invention
Figure.With reference to Fig. 6, the equipment of the electromagnetism Spacecraft formation hovering cooperative control method, including：Processor (processor) 61,
Memory (memory) 62 and bus 63；Wherein, the processor 61 and memory 62 are completed each other by the bus 63
Communication；The processor 61 is used to call the program instruction in the memory 62, to execute above-mentioned each method embodiment institute
The method of offer, such as including：For any one electromagnetism spacecraft, the electromagnetic coil installed on the electromagnetism spacecraft is generated
Electromagnetic field be regarded as dipole, establish electromagnetic force far field model, calculate in the model of electromagnetic force far field between each two electromagnetic coil
Electromagnetic force, obtain the first electromagnetic force accounting equation, and calculated suffered by the electromagnetism spacecraft according to the first electromagnetic force accounting equation
The electromagnetic force arrived obtains the second electromagnetic force accounting equation；Using with reference to the barycenter of spacecraft reference coordinate is established as coordinate origin
System, using the synperiodic circular orbit of elliptic orbit with reference to spacecraft movement as nominal track, based on mark under reference frame
Claim track to establish the electromagnetism spacecraft with reference to the target dynamics equation of Spacecraft Relative Motion, is based on target dynamics equation
Robust Control Law is designed using sliding-mode control；It is navigated to all electromagnetism according to the second electromagnetic force accounting equation and Robust Control Law
The magnetic moment of its device is allocated.
The present embodiment discloses a kind of computer program product, and the computer program product includes being stored in non-transient calculating
Computer program on machine readable storage medium storing program for executing, the computer program include program instruction, when described program instruction is calculated
When machine executes, computer is able to carry out the method that above-mentioned each method embodiment is provided, such as including：For any one electromagnetism
The electromagnetic field that the electromagnetic coil installed on the electromagnetism spacecraft generates is regarded as dipole, establishes electromagnetic force far field mode by spacecraft
Type calculates the electromagnetic force between each two electromagnetic coil in the model of electromagnetic force far field, obtains the first electromagnetic force accounting equation, and root
The electromagnetic force suffered by the electromagnetism spacecraft is calculated according to the first electromagnetic force accounting equation, obtains the second electromagnetic force accounting equation；It will
Reference frame is established as coordinate origin with reference to the barycenter of spacecraft, the elliptic orbit with reference to spacecraft movement is synperiodic
Circular orbit as nominal track, under reference frame based on nominal track establish the electromagnetism spacecraft with reference to spacecraft it is opposite
The target dynamics equation of movement designs Robust Control Law based on target dynamics equation using sliding-mode control；According to
Two electromagnetic force accounting equations and Robust Control Law are allocated the magnetic moment of all electromagnetism spacecrafts.
The present embodiment provides a kind of non-transient computer readable storage medium, the non-transient computer readable storage medium
Computer instruction is stored, the computer instruction makes the computer execute the method that above-mentioned each method embodiment is provided, example
Such as include：For any one electromagnetism spacecraft, the electromagnetic field that the electromagnetic coil installed on the electromagnetism spacecraft generates is regarded as
Dipole establishes electromagnetic force far field model, calculates the electromagnetic force between each two electromagnetic coil in the model of electromagnetic force far field, obtains
First electromagnetic force accounting equation, and the electromagnetic force suffered by the electromagnetism spacecraft is calculated according to the first electromagnetic force accounting equation, it obtains
Obtain the second electromagnetic force accounting equation；Reference frame is established as coordinate origin using with reference to the barycenter of spacecraft, space flight will be referred to
The synperiodic circular orbit of elliptic orbit of device movement establishes the electricity under reference frame as nominal track based on nominal track
Magnetic spacecraft uses sliding formwork control side with reference to the target dynamics equation of Spacecraft Relative Motion based on target dynamics equation
Method designs Robust Control Law；The magnetic moment of all electromagnetism spacecrafts is carried out according to the second electromagnetic force accounting equation and Robust Control Law
Distribution.
One of ordinary skill in the art will appreciate that：Realize that all or part of step of above method embodiment can pass through
The relevant hardware of program instruction is completed, and program above-mentioned can be stored in a computer read/write memory medium, the program
When being executed, step including the steps of the foregoing method embodiments is executed；And storage medium above-mentioned includes：ROM, RAM, magnetic disc or light
The various media that can store program code such as disk.
The embodiments such as the equipment of electromagnetism Spacecraft formation hovering cooperative control method described above are only schematic
, wherein the unit illustrated as separating component may or may not be physically separated, it is aobvious as unit
The component shown may or may not be physical unit, you can be located at a place, or may be distributed over multiple
In network element.Some or all of module therein can be selected according to the actual needs to realize the mesh of this embodiment scheme
's.Those of ordinary skill in the art are not in the case where paying performing creative labour, you can to understand and implement.
Through the above description of the embodiments, those skilled in the art can be understood that each embodiment can
It is realized by the mode of software plus required general hardware platform, naturally it is also possible to pass through hardware.Based on this understanding, on
Stating technical solution, substantially the part that contributes to existing technology can be expressed in the form of software products in other words, should
Computer software product can store in a computer-readable storage medium, such as ROM/RAM, magnetic disc, CD, including several fingers
It enables and using so that a computer equipment (can be personal computer, server or the network equipment etc.) executes each implementation
Method described in certain parts of example or embodiment.
Finally, the present processes are only preferable embodiment, are not intended to limit the scope of the present invention.It is all
Within the spirit and principles in the present invention, any modification, equivalent replacement, improvement and so on should be included in the protection of the present invention
Within the scope of.
Claims (10)
- The cooperative control method 1. a kind of electromagnetism Spacecraft formation hovers, which is characterized in that including：For any one electromagnetism spacecraft, the electromagnetic field that the electromagnetic coil installed on the electromagnetism spacecraft generates is regarded as dipole Son establishes electromagnetic force far field model, calculates the electromagnetic force between each two electromagnetic coil in the model of the electromagnetic force far field, obtains First electromagnetic force accounting equation, and the electromagnetism suffered by the electromagnetism spacecraft is calculated according to the first electromagnetic force accounting equation Power obtains the second electromagnetic force accounting equation；Reference frame is established as coordinate origin using with reference to the barycenter of spacecraft, by the oval rail moved with reference to spacecraft The synperiodic circular orbit in road establishes the electromagnetism space flight under the reference frame as nominal track based on the nominal track Device and the target dynamics equation with reference to Spacecraft Relative Motion use sliding formwork control based on the target dynamics equation Method designs Robust Control Law；The magnetic moment of all electromagnetism spacecrafts is carried out according to the second electromagnetic force accounting equation and the Robust Control Law Distribution.
- 2. according to the method described in claim 1, it is characterized in that, described be based on the nominal rail under the reference frame The electromagnetism spacecraft and the target dynamics equation with reference to Spacecraft Relative Motion are established in road, specially：Under the reference frame, the electromagnetism spacecraft and the candidate dynamics side with reference to Spacecraft Relative Motion are established Journey；By the elliptic orbit relative to the deviation of the nominal track, Earth nonspherical gravitation perturbation, solar light pressure, electromagnetic force The gravitation of far field model error and other celestial bodies is as Uncertainty, according to the Uncertainty by the candidate dynamics side Journey is converted to the target dynamics equation.
- 3. according to the method described in claim 1, it is characterized in that, described use sliding formwork control based on the target dynamics equation Method processed designs Robust Control Law, specially：Sliding surface is obtained according to the current state of the electromagnetism spacecraft and nominal state；Hitting control law and reaching condition are chosen, is set according to the Hitting control law and the reaching condition based on the sliding surface Count the Robust Control Law.
- 4. according to the method described in claim 1, it is characterized in that, described use sliding formwork control based on the target dynamics equation Method processed designs Robust Control Law, further includes later：The corresponding collaboration of the electromagnetism spacecraft is obtained according to the correspondence between the electromagnetism spacecraft and other electromagnetism spacecrafts , the collaboration item is added to the Robust Control Law, obtains coordination control laws.
- 5. according to the method described in claim 4, it is characterized in that, it is described according to the electromagnetism spacecraft in other electromagnetism spacecrafts Between correspondence obtain collaboration item, specially：Using each electromagnetism spacecraft as node, using the correspondence between each two electromagnetism spacecraft as side, and by every two Communication performance between a electromagnetism spacecraft establishes weighted undirected graph as adjacency matrix；The corresponding collaboration item of the electromagnetism spacecraft is obtained according to the weighted undirected graph.
- 6. according to the method described in claim 1, it is characterized in that, described according to the second electromagnetic force accounting equation and described Robust Control Law is allocated the magnetic moment of all electromagnetism spacecrafts, specially：For any one electromagnetism spacecraft, the Robust Control Law is substituted into the second electromagnetic force accounting equation and obtains the electricity The corresponding constraint equation of magnetic spacecraft；One external force is set, it is corresponding about that the external force is increased into an electromagnetism spacecraft in all electromagnetism spacecrafts In Shu Fangcheng；Object function is set based on energetic optimum and the principle of magnetic moment configuration equilibrium and track profile decoupling, according to all described The corresponding constraint equation of electromagnetism spacecraft and the object function are allocated the magnetic moment of all electromagnetism spacecrafts.
- 7. according to the method described in claim 6, it is characterized in that, the object function is specially：Wherein, uiIndicate the electromagnetic force that i spacecrafts are subject to；W1i、W2iIndicate weight coefficient matrix；τiIndicate i spacecrafts by The electromagnetic interference torque arrived；γiIt is the balancing coefficient of selection；f0Indicate external force；WoIt is its balancing coefficient matrix；N indicates all boats The total quantity of its device.
- The cooperative control system 8. a kind of electromagnetism Spacecraft formation hovers, which is characterized in that including：Electromagnetic force computing module is used for for any one electromagnetism spacecraft, the electromagnetic coil that will be installed on the electromagnetism spacecraft The electromagnetic field of generation is regarded as dipole, establishes electromagnetic force far field model, calculates each two electromagnetism in the model of the electromagnetic force far field Electromagnetic force between coil obtains the first electromagnetic force accounting equation, and calculates the electricity according to the first electromagnetic force accounting equation Electromagnetic force suffered by magnetic spacecraft obtains the second electromagnetic force accounting equation；Design of control law module, for the barycenter for referring to spacecraft to be established reference frame as coordinate origin, by the ginseng The synperiodic circular orbit of elliptic orbit of spacecraft movement is examined as nominal track, the mark is based under the reference frame Track is claimed to establish the electromagnetism spacecraft and the target dynamics equation with reference to Spacecraft Relative Motion, it is dynamic based on the target Mechanical equation designs Robust Control Law using sliding-mode control；Magnetic moment distribution module is used for according to the second electromagnetic force accounting equation and the Robust Control Law to all electromagnetism The magnetic moment of spacecraft is allocated.
- 9. a kind of equipment of electromagnetism Spacecraft formation hovering cooperative control method, which is characterized in that including：At least one processor；AndAt least one processor being connect with the processor communication, wherein：The memory is stored with the program instruction that can be executed by the processor, and the processor calls described program to instruct energy Enough methods executed as described in claim 1 to 7 is any.
- 10. a kind of non-transient computer readable storage medium, which is characterized in that the non-transient computer readable storage medium is deposited Computer instruction is stored up, the computer instruction makes the computer execute the method as described in claim 1 to 7 is any.
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| WO2020045180A1 (en) * | 2018-08-30 | 2020-03-05 | 国立研究開発法人宇宙航空研究開発機構 | Satellite position/attitude control system, and satellite position/attitude control method |
| CN113071713A (en) * | 2021-03-11 | 2021-07-06 | 中国空间技术研究院 | Satellite magnetic moment distribution method and device |
| CN115639830A (en) * | 2022-12-15 | 2023-01-24 | 北京航空航天大学 | Air-ground intelligent agent cooperative formation control system and formation control method thereof |
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| CN113071713B (en) * | 2021-03-11 | 2022-11-22 | 中国空间技术研究院 | Satellite magnetic moment distribution method and device |
| CN115639830A (en) * | 2022-12-15 | 2023-01-24 | 北京航空航天大学 | Air-ground intelligent agent cooperative formation control system and formation control method thereof |
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