CN108628345B - Electromagnetic spacecraft formation hovering cooperative control method and system - Google Patents

Electromagnetic spacecraft formation hovering cooperative control method and system Download PDF

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CN108628345B
CN108628345B CN201810688307.3A CN201810688307A CN108628345B CN 108628345 B CN108628345 B CN 108628345B CN 201810688307 A CN201810688307 A CN 201810688307A CN 108628345 B CN108628345 B CN 108628345B
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electromagnetic force
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CN108628345A (en
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师鹏
张亚博
雷冰瑶
何汉卿
赵育善
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Beihang University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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    • G05D1/10—Simultaneous control of position or course in three dimensions
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    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying

Abstract

The invention provides a hovering cooperative control method and a hovering cooperative control system for formation of an electromagnetic spacecraft, wherein the method comprises the following steps: for any electromagnetic spacecraft, calculating the electromagnetic force applied to the electromagnetic spacecraft to obtain an electromagnetic force calculation equation; taking the circular orbit with the same period as the elliptical orbit of the reference spacecraft as a nominal orbit, establishing a target kinetic equation of the relative motion of the electromagnetic spacecraft and the reference spacecraft, and designing a robust control law by adopting a sliding mode control method based on the target kinetic equation; and distributing the magnetic moments of all the electromagnetic spacecrafts according to an electromagnetic force calculation equation and a robust control law. The control law designed by the method and the system can also realize hovering of the formation of the electromagnetic spacecraft at any position in space under the condition that the electromagnetic spacecraft can not obtain real-time information of the reference orbit and is affected by various interference effects, so that the method and the system have good robustness; the optimized configuration of the magnetic moment of the electromagnetic spacecraft is realized by adopting an optimized method, and the decoupling of the orbit and the attitude of the electromagnetic spacecraft is facilitated.

Description

Electromagnetic spacecraft formation hovering cooperative control method and system
Technical Field
The invention relates to the technical field of communication, in particular to a method and a system for cooperative control of formation and hovering of an electromagnetic spacecraft.
Background
The formation hovering refers to a state that a plurality of accompanying spacecrafts in a gravitational field keep relatively static relative to a reference spacecraft or other natural celestial bodies under the action of control force. The formation hovering technology is widely applied to the fields of spacecraft on-orbit service, deep space exploration, spacecraft tracking monitoring and the like. When the hovering spacecraft is suspended at a close distance, the traditional thruster based on the impulse principle can cause plume pollution and has a limited service life, and some tasks can even strictly limit the ignition of a target in the direction of connecting the hovering spacecraft with the target. In addition, the non-keplerian nature of the member spacecraft hovering orbit in formation necessarily requires the thruster to work for a long time. The use of electromagnetic interactions to achieve relative orbital control between spacecraft has received attention from a number of scholars. The electromagnetic spacecraft changes the electromagnetic force applied to the spacecraft by changing the current of three orthogonal electromagnetic coils arranged on the electromagnetic spacecraft, so that the relative orbit control of the formation of the spacecraft is realized, and a new idea is provided for the realization of the control of the formation of the spacecraft.
The problems existing in the traditional thruster are well solved after the electromagnetic action is introduced, but the inherent nonlinearity, the interactivity and the uncertain interference of the space environment of the electromagnetic action determine that the formation control of the electromagnetic spacecraft has the characteristics of strong nonlinearity, strong coupling and uncertainty, and higher requirements are provided for the design of a controller.
Some research achievements have been made at home and abroad about the control of electromagnetic spacecraft formation, and Ahsun and the like respectively adopt an artificial potential function method and a nonlinear self-adaptive control method based on a circular reference orbit to research the configuration retention problem of the electromagnetic spacecraft formation, and provide a magnetic moment solving method by adding constraint or optimizing distribution. Kwon et al verified the feasibility of using superconducting coils to generate inter-satellite electromagnetic force for orbital tracking using ground experiments. Abbott et al, based on a sequential quadratic programming algorithm, given a semi-analytic method to solve for magnetic moment, assuming that the control acceleration is known. In addition, a large amount of research has been conducted by domestic scholars. The picror and the like provide a nonlinear feedback control method based on a double-spacecraft accurate relative motion model. The creep text and the like keep and design a self-adaptive control law for the configuration of the double-star electromagnetic spacecraft and provide an analytical expression of double-star magnetic moment distribution based on energy balance. The shore longfei research and other researches show that the formation control of the multi-electromagnetic spacecraft can be converted into the staged double-electromagnetic spacecraft control.
The existing research results can solve the problems of configuration maintenance and relative orbit attitude tracking of electromagnetic spacecraft formation to a certain extent, but the internal uncertainty of a dynamic model is less considered in the research, and the uncertainty is inevitable in the actual task. Furthermore, the control laws designed in the existing research results all require accurate information in real time with reference to the orbit, which is difficult or even impossible to obtain in some cases. In addition, most of the existing research results do not consider the communication among the member spacecrafts in the formation, and the relative state information of the member spacecrafts cannot be effectively utilized, so that the formation has poor coordination capability and generates redundant control.
Disclosure of Invention
The invention provides a method and a system for controlling formation hovering of an electromagnetic spacecraft in a coordinated manner, aiming at solving the problems that the control laws designed in the prior art are difficult to realize due to the fact that real-time accurate information of a reference orbit is needed, communication among member spacecrafts in the formation is not considered in the prior art, and relative state information of the member spacecrafts cannot be effectively utilized, so that the formation coordinating capability is poor and redundant control is generated.
In one aspect, the invention provides an electromagnetic spacecraft formation hovering cooperative control method, which comprises the following steps:
regarding any electromagnetic spacecraft, regarding an electromagnetic field generated by electromagnetic coils installed on the electromagnetic spacecraft as a dipole, establishing an electromagnetic force far-field model, calculating the electromagnetic force between every two electromagnetic coils in the electromagnetic force far-field model to obtain a first electromagnetic force calculation equation, and calculating the electromagnetic force applied to the electromagnetic spacecraft according to the first electromagnetic force calculation equation to obtain a second electromagnetic force calculation equation;
establishing a reference coordinate system by taking the mass center of a reference spacecraft as a coordinate origin, taking a circular orbit of the elliptical orbit of the reference spacecraft, which moves in the same period, as a nominal orbit, establishing a target kinetic equation of relative motion of the electromagnetic spacecraft and the reference spacecraft on the basis of the nominal orbit under the reference coordinate system, and designing a robust control law by adopting a sliding mode control method on the basis of the target kinetic equation;
and distributing the magnetic moments of all the electromagnetic spacecrafts according to the second electromagnetic force calculation equation and the robust control law.
Preferably, the establishing of the target kinetic equation of the relative motion of the electromagnetic spacecraft and the reference spacecraft based on the nominal orbit in the reference coordinate system specifically includes:
establishing a candidate kinetic equation of relative motion of the electromagnetic spacecraft and the reference spacecraft under the reference coordinate system;
and converting the candidate kinetic equation into the target kinetic equation according to the uncertainty by taking the deviation of the elliptical orbit relative to the nominal orbit, the perturbation of the earth's non-spherical gravity, the sunlight pressure, the error of the electromagnetic force far-field model and the gravity of other celestial bodies as uncertainty.
Preferably, the robust control law is designed by adopting a sliding mode control method based on the target kinetic equation, and specifically comprises the following steps:
acquiring a sliding surface according to the current state and the nominal state of the electromagnetic spacecraft;
and selecting an arrival control law and an arrival condition, and designing the robust control law according to the arrival control law and the arrival condition on the basis of the sliding surface.
Preferably, the robust control law is designed by adopting a sliding mode control method based on the target kinetic equation, and then the method further includes:
and obtaining a cooperative item corresponding to the electromagnetic spacecraft according to the communication relation between the electromagnetic spacecraft and other electromagnetic spacecrafts, and adding the cooperative item to the robust control law to obtain a cooperative control law.
Preferably, the obtaining of the collaborative item according to the communication relationship between the electromagnetic spacecraft and the other electromagnetic spacecraft specifically includes:
taking each electromagnetic spacecraft as a node, taking the communication relation between every two electromagnetic spacecrafts as an edge, taking the communication performance between every two electromagnetic spacecrafts as an adjacency matrix, and establishing a weighted undirected graph;
and obtaining the corresponding cooperative item of the electromagnetic spacecraft according to the weighted undirected graph.
Preferably, the allocating magnetic moments of all the electromagnetic spacecrafts according to the second electromagnetic force calculation equation and the robust control law specifically includes:
for any electromagnetic spacecraft, substituting the robust control law into the second electromagnetic force calculation equation to obtain a constraint equation corresponding to the electromagnetic spacecraft;
setting an external force, and adding the external force to a constraint equation corresponding to one of all the electromagnetic spacecrafts;
and setting a target function based on the principles of energy optimization, magnetic moment configuration balance and orbit attitude decoupling, and distributing the magnetic moments of all the electromagnetic spacecrafts according to constraint equations corresponding to all the electromagnetic spacecrafts and the target function.
Preferably, the objective function is specifically:
Figure BDA0001712254290000041
Figure BDA0001712254290000042
wherein u isiRepresenting the electromagnetic force suffered by the No. i spacecraft; w1i、W2iRepresenting a weight coefficient matrix; tau isiRepresenting the electromagnetic interference moment suffered by the spacecraft No. i; gamma rayiIs the selected trim factor; f. of0Represents an external force; woIs its trim coefficient matrix; n represents the total number of all spacecraft.
In one aspect, the present invention provides an electromagnetic spacecraft formation hovering cooperative control system, including:
the electromagnetic force calculation module is used for regarding an electromagnetic field generated by electromagnetic coils arranged on any electromagnetic spacecraft as a dipole, establishing an electromagnetic force far field model, calculating the electromagnetic force between every two electromagnetic coils in the electromagnetic force far field model to obtain a first electromagnetic force calculation equation, and calculating the electromagnetic force applied to the electromagnetic spacecraft according to the first electromagnetic force calculation equation to obtain a second electromagnetic force calculation equation;
the control law design module is used for establishing a reference coordinate system by taking the mass center of a reference spacecraft as a coordinate origin, taking a circular orbit of the same period of an elliptical orbit of the motion of the reference spacecraft as a nominal orbit, establishing a target kinetic equation of the relative motion of the electromagnetic spacecraft and the reference spacecraft on the basis of the nominal orbit under the reference coordinate system, and designing a robust control law by adopting a sliding mode control method on the basis of the target kinetic equation;
and the magnetic moment distribution module is used for distributing the magnetic moments of all the electromagnetic spacecrafts according to the second electromagnetic force calculation equation and the robust control law.
In one aspect, the present invention provides an apparatus of a method for cooperative control of formation and hovering of an electromagnetic spacecraft, including:
at least one processor; and
at least one memory communicatively coupled to the processor, wherein:
the memory stores program instructions executable by the processor, the processor being capable of performing any of the methods described above when invoked by the processor.
In one aspect, the present invention provides a non-transitory computer readable storage medium storing computer instructions that cause a computer to perform any of the methods described above.
According to the formation and hovering cooperative control method and system for the electromagnetic spacecraft, for any electromagnetic spacecraft, an electromagnetic field generated by electromagnetic coils installed on the electromagnetic spacecraft is regarded as a dipole, an electromagnetic force far-field model is established, the electromagnetic force between every two electromagnetic coils in the electromagnetic force far-field model is calculated, a first electromagnetic force calculation equation is obtained, the electromagnetic force applied to the electromagnetic spacecraft is calculated according to the first electromagnetic force calculation equation, and a second electromagnetic force calculation equation is obtained; establishing a reference coordinate system by taking the mass center of a reference spacecraft as a coordinate origin, taking a circular orbit of the same period of an elliptical orbit of the motion of the reference spacecraft as a nominal orbit, establishing a target kinetic equation of the relative motion of the electromagnetic spacecraft and the reference spacecraft, and designing a robust control law by adopting a sliding mode control method based on the target kinetic equation; and distributing the magnetic moments of all the electromagnetic spacecrafts according to a second electromagnetic force calculation equation and a robust control law. The method and the system design a robust cooperative control for the orbit hovering of the electromagnetic spacecraft formation system, so that the electromagnetic spacecraft formation can be hovered at any position in space under the condition that the electromagnetic spacecraft cannot obtain real-time information of the reference orbit and is subjected to various interference effects, and the robustness is good. On the basis of the control, the optimized configuration of the magnetic moments of the formation of the electromagnetic spacecraft is realized by adopting an optimized method, and the magnetic moments obtained through the optimization are beneficial to decoupling of the orbit and the attitude of the electromagnetic spacecraft.
Drawings
Fig. 1 is a schematic overall flow chart of an electromagnetic spacecraft formation hovering cooperative control method according to an embodiment of the present invention;
FIG. 2 is a schematic illustration of the interaction of two electromagnetic coils on an electromagnetic spacecraft of an embodiment of the present invention;
FIG. 3 is a diagram illustrating magnetic dipole interactions in a far-field model of electromagnetic force according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a formation hovering configuration of an electromagnetic spacecraft in a simulation experiment according to an embodiment of the present invention;
FIG. 5 is a schematic overall structure diagram of an electromagnetic spacecraft formation hovering cooperative control system according to an embodiment of the present invention;
fig. 6 is a structural framework schematic diagram of an apparatus of an electromagnetic spacecraft formation hover cooperative control method according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
It should be noted that, hovering in formation refers to a state in which a plurality of accompanying spacecraft in a gravitational field are kept relatively still with respect to a reference spacecraft or other natural celestial bodies under the control force. The invention selects the electromagnetic spacecraft as the accompanying spacecraft, namely the electromagnetic spacecraft in the invention refers to the accompanying spacecraft. On the basis, the robust cooperative control is designed for the orbit hovering of the electromagnetic spacecraft formation system, so that the electromagnetic spacecraft formation hovering at any space position is realized under the condition that member spacecrafts cannot acquire real-time information of the reference orbit and are subjected to various interference effects. And on the basis of the control, the optimized configuration of the electromagnetic spacecraft formation magnetic moment is realized by adopting an optimization method based on the indexes of energy saving and consumption balance. The specific implementation process is as follows:
fig. 1 is a schematic overall flow chart of an electromagnetic spacecraft formation hover cooperative control method according to an embodiment of the present invention, and as shown in fig. 1, the present invention provides an electromagnetic spacecraft formation hover cooperative control method, including:
s1, regarding an electromagnetic field generated by electromagnetic coils installed on any electromagnetic spacecraft as a dipole, establishing an electromagnetic force far-field model, calculating the electromagnetic force between every two electromagnetic coils in the electromagnetic force far-field model to obtain a first electromagnetic force calculation equation, and calculating the electromagnetic force applied to the electromagnetic spacecraft according to the first electromagnetic force calculation equation to obtain a second electromagnetic force calculation equation;
specifically, three orthogonal electromagnetic coils are installed on each electromagnetic spacecraft, electromagnetic force and electromagnetic torque which interact with each other can be generated after the coils are electrified, and orbital maneuver and attitude adjustment of the electromagnetic spacecraft can be realized by utilizing the force and the torque. The interaction between the electromagnetic coils is related to the distance between the coil centers and the spatial orientation of the coils. The electromagnetic force and the electromagnetic torque between the two electrified coils can be accurately calculated by adopting the Biao-Saval law. As shown in FIG. 2, when the coil 2 is located in the electromagnetic field of the coil 1, the current infinitesimal of the coil 2 is integrated in the electromagnetic field of the coil 1, and the electromagnetic force F of the coil 1 on the coil 2 can be obtained2Sum torque T2While F is2And T2That is, the electromagnetic force and the electromagnetic moment between the coil 1 and the coil 2, the following equations (1) and (2) are specifically solved:
Figure BDA0001712254290000071
Figure BDA0001712254290000072
wherein, mu0Is a vacuum magnetic permeability, and mu0＝4π×10-7N×A-2；i1And i2Respectively represent the current applied to coil 1 and coil 2; a is1And a2The radii of coil 1 and coil 2 are indicated, respectively; dl (dl)1And dl2Respectively representing the length infinitesimal of the coil 1 and the coil 2; d represents the distance between the length bins of the two coils.
The precise electromagnetic force formula obtained by the integration is complex in form and is not easy to be directly applied in engineering. Researches find that when the distance between the two coils is larger than 8 times of the diameter of the coil, a far-field electromagnetic force model obtained by taking an electromagnetic field generated by the coil as a dipole can also meet the precision requirement in engineering. In view of this, in this embodiment, for any electromagnetic spacecraft, the electromagnetic field generated by the electromagnetic coil installed on the electromagnetic spacecraft is regarded as a dipole, and an electromagnetic force far-field model is established, as shown in fig. 3, in the electromagnetic force far-field model, the electromagnetic field of the coil is regarded as a dipole, the magnitude and direction of which are described by magnetic moments, and the solving formula of the magnetic moment u is as follows (3):
μ＝NISn (3)
n is the number of turns of the coil, I is the current value, S is the area of the coil, and N is the unit vector of the normal direction of the current-carrying plane, and obeys the right-hand rule.
In the electromagnetic force far field model, the electromagnetic force F between the two coils2And electromagnetic torque T2The following equations (4) and (5) can be used for calculation, respectively:
Figure BDA0001712254290000081
Figure BDA0001712254290000082
wherein, mu0Is a vacuum magnetic conductivity; u. of1And u2Respectively representing the magnetic moments of coil 1 and coil 2; r represents the distance between the centers of the two coils; the above equation (4) is the first electromagnetic force calculation equation. Therefore, the electromagnetic force applied to each electromagnetic coil in the spacecraft can be calculated according to the first electromagnetic force calculation equation. On the basis, the electromagnetic force applied to the three electromagnetic coils on the spacecraft is summed to obtain the electromagnetic force applied to the whole electromagnetic spacecraft. Assuming that the formation system has N electromagnetic spacecrafts, numbered i ═ 1,2,3, …, N, the electromagnetic spacecrafts can generate magnetic moments in any directions. For the electromagnetic spacecraft with the number i, the electromagnetic force applied to the electromagnetic spacecraft can be obtained through a second electromagnetic force calculation equation, wherein the second electromagnetic force calculation equation is specifically as follows (6):
Figure BDA0001712254290000083
wherein, FiThe spacecraft numbered i is subjected to the resultant force of the electromagnetic forces, FijRepresents the electromagnetic action of the j spacecraft on the i spacecraft, mui、μjRespectively representing the magnetic moments, r, of spacecraft No. i and spacecraft No. jijAnd the position of the spacecraft I relative to the spacecraft j is shown, and the spacecraft i points to the spacecraft j.
S2, establishing a reference coordinate system by taking the mass center of the reference spacecraft as a coordinate origin, taking a circular orbit of the same period of an elliptical orbit of the reference spacecraft as a nominal orbit, establishing a target kinetic equation of relative motion of the electromagnetic spacecraft and the reference spacecraft based on the nominal orbit under the reference coordinate system, and designing a robust control law by adopting a sliding mode control method based on the target kinetic equation;
specifically, in order to describe the relative motion between the electromagnetic spacecrafts, a geocentric inertial coordinate system is introduced, the origin of coordinates of the geocentric inertial coordinate system is located at the center of the earth, the X axis of the geocentric inertial coordinate system is located on the equatorial plane and points to the vernal equinox direction, the Z axis is perpendicular to the equatorial plane and points to the north pole, and the Y axis, the X axis and the Z axis form a right-handed system. On the basis, a reference coordinate system is established by taking the mass center of the reference spacecraft as a coordinate origin, the x axis of the reference coordinate system points to the mass center of the reference spacecraft from the earth center along the radial direction and is positive, the y axis is vertical to the x axis in the orbital plane and points to the forward direction of the satellite and is positive, and the z axis, the x axis and the y axis form a right-hand coordinate system.
On the basis, if the control is not exerted on the reference spacecraft and the distance between the electromagnetic spacecrafts in the formation is far smaller than the distance from the centroid of the reference spacecraft to the geocentric, a kinetic equation of the relative motion between the electromagnetic spacecrafts and the reference spacecraft in the hovering formation can be established under the reference coordinate system. However, the variation parameters in the above dynamic equations are all related to the reference orbit where the reference spacecraft is located, and if the control law is designed according to the above dynamic equations, real-time accurate information of the reference orbit needs to be obtained, which is difficult or even impossible to obtain in some cases.
In view of this, in the embodiment, circular orbits of the same period as the elliptical orbit (reference orbit) of the reference spacecraft motion are used as the nominal orbits, and on the basis, the deviation of the elliptical orbit relative to the nominal circular orbit, the earth aspheric perturbation interference, the air resistance and the like are separately classified and treated as uncertain factors. Thereby, the above kinetic equation is converted into a target kinetic equation.
On the basis, a robust control law is designed by adopting a sliding mode control method based on the obtained target kinetic equation. The formation and hovering of the electromagnetic spacecraft can be realized according to the robust control law. The principle of the sliding mode control is to design a switching hyperplane of the system according to the dynamic characteristics expected by the system, and the system state is converged from the outside of the hyperplane to the switching hyperplane by the sliding mode controller. Once the system reaches the switching hyperplane, the control action ensures that the system reaches the system origin along the switching hyperplane, and the process of sliding to the origin along the switching hyperplane is called sliding mode control. The characteristics and parameters of the system only depend on the designed switching hyperplane and have no relation with external interference, so the sliding mode variable structure control has strong robustness.
And S3, distributing the magnetic moments of all the electromagnetic spacecrafts according to the second electromagnetic force calculation equation and the robust control law.
Specifically, as can be seen from the second electromagnetic force calculation equation, the second electromagnetic force calculation equation can represent the relationship between the electromagnetic force and the magnetic moment applied to the electromagnetic spacecraft. In order to realize formation and hovering of the electromagnetic spacecraft, the electromagnetic force applied to the electromagnetic spacecraft should be consistent with the robust control law obtained above. Therefore, on the basis of obtaining the robust control law, after the robust control law is substituted into the second electromagnetic force equation, the magnetic moment corresponding to each electromagnetic spacecraft can be calculated through an optimization method. In the embodiment, in addition to the energy consumption optimization and balance, the moment generated by the electromagnetic coil and the external force required by the formation mass center of the motor spacecraft are also considered in the optimization method. Therefore, the magnetic moment distribution of all the electromagnetic spacecrafts can be realized.
According to the formation and hovering cooperative control method for the electromagnetic spacecrafts, for any electromagnetic spacecraft, an electromagnetic field generated by electromagnetic coils installed on the electromagnetic spacecrafts is regarded as a dipole, an electromagnetic force far-field model is established, the electromagnetic force between every two electromagnetic coils in the electromagnetic force far-field model is calculated, a first electromagnetic force calculation equation is obtained, the electromagnetic force borne by the electromagnetic spacecrafts is calculated according to the first electromagnetic force calculation equation, and a second electromagnetic force calculation equation is obtained; establishing a reference coordinate system by taking the mass center of a reference spacecraft as a coordinate origin, taking a circular orbit of the same period of an elliptical orbit of the motion of the reference spacecraft as a nominal orbit, establishing a target kinetic equation of the relative motion of the electromagnetic spacecraft and the reference spacecraft, and designing a robust control law by adopting a sliding mode control method based on the target kinetic equation; and distributing the magnetic moments of all the electromagnetic spacecrafts according to a second electromagnetic force calculation equation and a robust control law. The method designs robust cooperative control for the orbit hovering of the electromagnetic spacecraft formation system, so that the electromagnetic spacecraft formation hovering at any spatial position can be realized under the condition that the electromagnetic spacecraft cannot obtain real-time information of the reference orbit and is subjected to various interference effects, and the robustness is good. On the basis of the control, the optimized configuration of the magnetic moments of the formation of the electromagnetic spacecraft is realized by adopting an optimized method, and the magnetic moments obtained through the optimization are beneficial to decoupling of the orbit and the attitude of the electromagnetic spacecraft.
Based on any one of the embodiments, a hovering cooperative control method for formation of an electromagnetic spacecraft is provided, and a target kinetic equation of relative motion of the electromagnetic spacecraft and a reference spacecraft is established based on a nominal orbit in a reference coordinate system, specifically: establishing a candidate kinetic equation of relative motion of the electromagnetic spacecraft and the reference spacecraft under a reference coordinate system; and taking the deviation of the elliptical orbit relative to the nominal orbit, the earth aspheric gravitational perturbation, the sunlight pressure, the electromagnetic force far field model error and the gravitational force of other celestial bodies as uncertain quantities, and converting the candidate kinetic equation into a target kinetic equation according to the uncertain quantities.
Specifically, after a reference coordinate system is established with the centroid of the reference spacecraft as a coordinate origin, assuming that no control is applied to the reference spacecraft and the distance between the electromagnetic spacecrafts in the formation is far less than the distance from the centroid of the reference spacecraft to the geocentric, under the reference coordinate system, the candidate kinetic equation of the relative motion between the electromagnetic spacecrafts in the hovering formation and the reference spacecraft is as follows:
Figure BDA0001712254290000111
where the subscript i ═ 1,2,3, …, N denotes the number of the spacecraft in the hover formation, ρi＝[xiyizi]TRepresenting the position of the hovering spacecraft i in an orbital coordinate system. u. ofmhiIndicating the electromagnetic force, u, experienced by the hovering spacecraft idhiRepresenting external perturbations experienced by a hovering spacecraft i, including electromagnetic modeling inaccuracies, aerodynamic forces, solar pressure and other perturbations due to celestial gravity, udoRepresenting external perturbations to which the reference spacecraft is subjected, including aerodynamic, solar pressure perturbations and other celestial gravitations. Coefficient matrix D in the above equationeAnd KeRespectively as follows:
Figure BDA0001712254290000112
wherein R represents the center of mass of the reference spacecraftDistance to the center of the earth, omega,
Figure BDA0001712254290000113
Respectively, the orbital angular velocity and the angular acceleration of the reference spacecraft.
The candidate kinetic equation is a differential equation with time-varying coefficients, the parameters varying in the equation are all related to the elliptical orbit (reference orbit) of the reference spacecraft, and if a control law is designed according to the candidate kinetic equation, real-time accurate information of the reference orbit needs to be acquired, but the method is difficult to achieve in some cases. In view of this, in the present embodiment, a circular orbit having the same period as the elliptical orbit is used as the nominal orbit, and the deviation of the elliptical orbit from the nominal orbit, the perturbation of the earth's aspherical attraction, the solar pressure, the error of the electromagnetic force far-field model, and the attraction of other celestial bodies are used as uncertainties. Therefore, substituting the uncertain quantity into the candidate kinetic equation can obtain the target kinetic equation, which is specifically as follows:
Figure BDA0001712254290000121
wherein u isdi＝udhi-udoRepresenting an external uncertainty of the hovering spacecraft relative to the reference spacecraft relative motion model; Δ D includes deviation of the elliptical orbit from the nominal orbit and perturbation of the kinetic equation parameters, and Δ K includes deviation of the elliptical orbit from the nominal orbit and perturbation due to earth's non-spherical gravity and perturbation of the kinetic equation parameters. Since the radius of the circular orbit having the same period as the elliptical orbit is the semimajor axis of the ellipse, the matrix D in the above formulac、KcThe values of (A) are respectively:
Figure BDA0001712254290000122
meanwhile, the upper bound of the uncertainty matrix may be expressed as:
Figure BDA0001712254290000123
Figure BDA0001712254290000124
|udi|≤f(x,t)，f(x,t)≥0
wherein, αiAnd βjAre all perturbation parameters; eiAnd FjAre perturbation matrices; f (x, t) represents an upper bound function of the external uncertainty; a isiAnd bjAre respectively αiAnd βjThe upper bound of (c).
After the processing, the control law designed according to the target kinetic equation does not need real-time accurate information of the elliptical reference orbit, and the realization on engineering is facilitated. In addition, the target kinetic equation considers all internal and external uncertain factors causing the orbit deviation of the spacecraft, so that the designed control law has stronger robustness.
The invention provides a formation hovering cooperative control method for an electromagnetic spacecraft, which comprises the steps of establishing a candidate kinetic equation of relative motion of the electromagnetic spacecraft and a reference spacecraft under a reference coordinate system; and taking the deviation of the elliptical orbit relative to the nominal orbit as an uncertain quantity, and converting the candidate kinetic equation into a target kinetic equation according to the uncertain quantity, so that a control law can be designed according to the target kinetic equation. The target kinetic equation established by the method considers all internal and external uncertain factors causing spacecraft orbit deviation, and the control law designed according to the target kinetic equation does not need real-time accurate information of the elliptical reference orbit any more, so that the method has stronger robustness.
Based on any one of the embodiments, a hovering cooperative control method for electromagnetic spacecraft formation is provided, a robust control law is designed by adopting a sliding mode control method based on a target dynamics equation, and the method specifically comprises the following steps: acquiring a sliding surface according to the current state and the nominal state of the electromagnetic spacecraft; and selecting an arrival control law and an arrival condition, and designing a robust control law according to the arrival control law and the arrival condition on the basis of the sliding surface.
Specifically, the current electromagnetic spacecraft is obtained on the basis of establishing a target dynamic equationA state and a nominal state. Taking an electromagnetic spacecraft i as an example, the nominal state is
Figure BDA0001712254290000131
The deviation between the current state and the nominal state can be determined as
Figure BDA0001712254290000132
Selecting a sliding surface SiThe sliding surface function is specifically as follows:
Figure BDA0001712254290000133
wherein Λ ═ diag { λ r }, λ r >0, and r ═ 1,2, 3. It will be readily seen that the state motion on the sliding surface is stable, and then the design arrival motion is derived from the above sliding surface function to obtain the following:
Figure BDA0001712254290000134
because the formation hovering problem of the electromagnetic spacecraft is considered, the method has the advantages that
Figure BDA0001712254290000135
On this basis, the above formula (8) can be simplified to the following formula (9):
Figure BDA0001712254290000136
on the basis of the above, the arrival control law is selected as follows:
Figure BDA0001712254290000137
wherein HiAnd εiAre all matrix parameters.
To eliminate the jitter of the sliding motion on the sliding mode surface, a saturation function sat (x) is selected instead of the sign function. The function sat (x) is specified as follows:
Figure BDA0001712254290000141
the two equations of the comparison (9) and (10) are equivalently controlled as follows:
Figure BDA0001712254290000142
the control of the equation (11) has an indeterminate parameter and cannot be used as it is, and in order to remove the indeterminate parameter, the control of the equation (12) is first used instead.
Figure BDA0001712254290000143
To determine z1i、z2iThe above formula (12) is substituted into the above formula (9) to obtain the following formula (13).
Figure BDA0001712254290000144
The selection of the arrival conditions is as follows:
Figure BDA0001712254290000145
the write component form yields the following formula:
Figure BDA0001712254290000146
where the superscript r is 1,2,3 denotes the r-th component of the vector, vr(ii) (. denotes. the r-th row of the matrix, if taken
Figure BDA0001712254290000147
Figure BDA0001712254290000148
And (16) and (17) are brought into (15), the sizes of the items are compared, and the uncertain items are eliminated, so that the reaching condition (14) is met.
Equations (12), (16) and (17) form a control law for hovering of electromagnetic spacecraft formation, which can realize hovering tasks of electromagnetic spacecraft formation and has strong robustness to uncertain interference.
The invention provides a hovering cooperative control method for formation of an electromagnetic spacecraft, which comprises the steps of obtaining a sliding surface according to the current state and the nominal state of the electromagnetic spacecraft; and selecting an arrival control law and an arrival condition, and designing a robust control law according to the arrival control law and the arrival condition on the basis of the sliding surface. The control law obtained by the method does not need real-time accurate information of the elliptical reference orbit any more, and has stronger robustness.
Based on any one of the embodiments, the method for cooperative control of formation and hovering of the electromagnetic spacecraft is provided, a robust control law is designed by adopting a sliding mode control method based on a target dynamics equation, and then the method further comprises the following steps: and obtaining a cooperative item corresponding to the electromagnetic spacecraft according to the communication relation between the electromagnetic spacecraft and other electromagnetic spacecrafts, and adding the cooperative item to a robust control law to obtain the cooperative control law.
Specifically, the designed robust control law only considers the position and speed deviation information of the electromagnetic spacecraft in the formation, the state information of other electromagnetic spacecraft is not used, and the designed robust control law can only achieve good local performance from the aspect of a formation system and is examined from a global view, so that control waste exists.
In view of this, in the embodiment, the robust control law is improved to realize global coordination by using information exchange between electromagnetic spacecrafts. Specifically, a cooperative item corresponding to a certain electromagnetic spacecraft is obtained according to a communication relationship between the electromagnetic spacecraft and other electromagnetic spacecrafts, and the cooperative item is added to the robust control law, so that the cooperative control law can be obtained. The cooperative control law can effectively improve the cooperative performance among the electromagnetic spacecrafts in the formation system.
According to the electromagnetic spacecraft formation hovering cooperative control method provided by the invention, after a robust control law is designed by adopting a sliding mode control method based on a target dynamics equation, a cooperative item corresponding to an electromagnetic spacecraft is obtained according to a communication relation between the electromagnetic spacecraft and other electromagnetic spacecrafts, and the cooperative item is added to the robust control law to obtain the cooperative control law. The cooperative control law obtained by the method can effectively improve the cooperative performance among the electromagnetic spacecrafts in the formation system, and is beneficial to reducing the control waste.
Based on any of the embodiments, a coordinated control method for formation and hovering of an electromagnetic spacecraft is provided, where a coordinated item is obtained according to a communication relationship between the electromagnetic spacecraft and other electromagnetic spacecrafts, and the method specifically includes: taking each electromagnetic spacecraft as a node, taking the communication relation between every two electromagnetic spacecrafts as an edge, taking the communication performance between every two electromagnetic spacecrafts as an adjacency matrix, and establishing a weighted undirected graph; and obtaining the corresponding cooperative item of the electromagnetic spacecraft according to the weighted undirected graph.
In particular, the relevant concepts of graph theory are introduced here for the purpose of clearly describing the relationship between member spacecraft in a formation of spacecraft. A weighted undirected graph G (V, E, a) is formed from a set of nodes V ═ 1,2, …, N, and a set of edges
Figure BDA0001712254290000162
And the weighted adjacency matrix a ═ a [ ij ═ a [ ]]And (4) forming. The nodes represent the electromagnetic spacecrafts in the formation, the edges represent the communication relation among the electromagnetic spacecrafts in the formation, and the adjacency matrix represents the communication performance of the electromagnetic spacecrafts in the formation. If communication can be carried out between two spacecrafts i and j in the undirected graph, the edge (j, i) belongs to E and aij＝aji>0, otherwise aij0. It is generally assumed that the spacecraft and itself do not have communication, i.e. aii0. An undirected graph is said to be connected if a path exists between any two nodes in the graph.
On the basis of the graph theory, considering the communication delay among the electromagnetic spacecrafts in the formation, a synergistic term is added to the robust control law to obtain the synergistic control law as follows:
Figure BDA0001712254290000161
wherein, tauijRepresenting the communication latency between spacecraft i and spacecraft j.
The invention provides a formation hovering cooperative control method for electromagnetic spacecrafts, which comprises the steps of taking each electromagnetic spacecraft as a node, taking a communication relation between every two electromagnetic spacecrafts as an edge, taking the communication performance between every two electromagnetic spacecrafts as an adjacency matrix, and establishing a weighted undirected graph; and obtaining a cooperative item corresponding to the electromagnetic spacecraft according to the weighted undirected graph, and further adding the cooperative item to a robust control law to obtain the cooperative control law. The communication delay among the electromagnetic spacecrafts in the formation is considered by the cooperative items obtained by the method, and the cooperative performance among the electromagnetic spacecrafts in the formation system can be effectively improved by the obtained cooperative control law.
Based on any one of the embodiments, a coordinated control method for formation and hovering of electromagnetic spacecrafts is provided, magnetic moments of all electromagnetic spacecrafts are distributed according to a second electromagnetic force calculation equation and a robust control law, and the method specifically comprises the following steps: for any electromagnetic spacecraft, substituting the robust control law into a second electromagnetic force calculation equation to obtain a constraint equation corresponding to the electromagnetic spacecraft; setting an external force, and adding the external force to a constraint equation corresponding to one electromagnetic spacecraft of all the electromagnetic spacecrafts; and setting a target function based on the principles of energy optimization, magnetic moment configuration balance and orbit attitude decoupling, and distributing the magnetic moments of all the electromagnetic spacecrafts according to constraint equations and the target function corresponding to all the electromagnetic spacecrafts.
Specifically, for any electromagnetic spacecraft, after obtaining a second electromagnetic force calculation equation and a robust control law corresponding to the electromagnetic spacecraft, in order to achieve formation and hovering, the robust control law corresponding to the electromagnetic spacecraft needs to be balanced with the electromagnetic force to which the electromagnetic spacecraft is subjected. In view of this, the robust control law is substituted into the second electromagnetic force calculation equation to obtain the constraint equation corresponding to the electromagnetic spacecraft. Therefore, only magnetic moment variables exist in the constraint equation, and on the basis, the magnetic moment variables in the equation can be solved by combining the constraint equations corresponding to all electromagnetic spacecrafts so as to realize magnetic moment distribution.
However, since the resultant force of the electromagnetic forces applied to the whole formation system is zero, obviously, under the condition of only the interactive electromagnetic forces, the center of mass of the system cannot be changed, and hovering at any position cannot be realized. Thereby, the external force is added to a certain constraint equation.
On the basis of the above, it is assumed that the formation system has N electromagnetic space vehicles, where i is 1,2,3, …, and N is the second electromagnetic force calculation equation corresponding to the space vehicle numbered i, which is specifically as follows:
Figure BDA0001712254290000171
assuming that the external force is applied to the spacecraft N, the second electromagnetic force calculation equation corresponding to the spacecraft N is as follows:
Figure BDA0001712254290000172
wherein f isoRepresenting the external force exerted on spacecraft number N.
From the above analysis, it can be seen that the electromagnetic spacecraft formation system is subjected to independent constraints of 3N in total, but the independent variables are 3N +3 (including 3N magnetic moment variables and 3 external force variables), so that the system variables have redundant degrees of freedom, and the problem can be converted into an optimization problem with constraints for solving. In the embodiment, in order to enable the magnetic moment energy consumption and the external force fuel of the electromagnetic spacecraft to be more balanced, the objective function is set based on the principles of energy optimization, magnetic moment configuration balance and orbit attitude decoupling, and then all magnetic moment variables are solved according to the constraint equations and the objective functions corresponding to all the electromagnetic spacecrafts, so that the magnetic moments of all the electromagnetic spacecrafts can be distributed.
The invention provides a formation hovering cooperative control method for electromagnetic spacecrafts, which is characterized in that for any electromagnetic spacecraft, a robust control law is substituted into a second electromagnetic force calculation equation to obtain a constraint equation corresponding to the electromagnetic spacecraft; setting an external force, and adding the external force to a constraint equation corresponding to one electromagnetic spacecraft of all the electromagnetic spacecrafts; and setting a target function based on the principles of energy optimization, magnetic moment configuration balance and orbit attitude decoupling, and distributing the magnetic moments of all the electromagnetic spacecrafts according to constraint equations and the target function corresponding to all the electromagnetic spacecrafts. The method considers the optimal and balanced energy consumption and also considers the moment generated by the electromagnetic coil and the external force required by the formation mass center of the maneuvering spacecraft, and the magnetic moment obtained through the optimization is beneficial to decoupling of the orbit and the attitude of the electromagnetic spacecraft.
Based on any one of the embodiments, a cooperative control method for formation and hovering of an electromagnetic spacecraft is provided, where an objective function specifically is:
Figure BDA0001712254290000181
Figure BDA0001712254290000182
wherein u isiRepresenting the electromagnetic force suffered by the No. i spacecraft; w1i、W2iRepresenting a weight coefficient matrix; tau isiRepresenting the electromagnetic interference moment suffered by the spacecraft No. i; gamma rayiIs the selected trim factor; f. of0Represents an external force; woIs its trim coefficient matrix; n represents the total number of all spacecraft.
According to the electromagnetic spacecraft formation hovering cooperative control method provided by the invention, the target function is set based on the principles of energy optimization, magnetic moment configuration balance and orbit attitude decoupling, and then the magnetic moments of all electromagnetic spacecrafts are distributed according to the constraint equations and the target functions corresponding to all electromagnetic spacecrafts. The method considers the optimal and balanced energy consumption and also considers the moment generated by the electromagnetic coil and the external force required by the formation mass center of the maneuvering spacecraft, and the magnetic moment obtained through the optimization is beneficial to decoupling of the orbit and the attitude of the electromagnetic spacecraft.
To verify the aboveThe performance of the control law designed in any of the embodiments is a simulation calculation of a formation formed by 4 electromagnetic spacecrafts, and the formation configuration adopted by the formation of the spacecrafts is shown in fig. 4. At the initial moment, A, B, C and D total 4 spacecraft were located on 4 vertices of a regular tetrahedron with a ridge length of 15m, and the reference spacecraft was located at the center of the regular tetrahedron. The position and velocity of the member spacecraft are assumed to be perturbed somewhat randomly. The mass of the member spacecrafts in the formation is 100kg, the coil radius is 1m, and the number of coil turns of 4 spacecrafts is 100. The parameter of the controller is selected to be Hi＝10-2×I3×3、εi＝10-7×I3×3、Λi＝10-2×I3×3. Considering electromagnetic force modeling error, earth J2 perturbation, earth magnetic field perturbation, other celestial body perturbation and sunlight pressure, the upper bound of the formula uncertainty parameter is ai＝10-5、bj＝10-7、f＝10-7. Three spacecrafts are linked to form a ring, the other spacecraft is connected into the communication topological structure of the triangular ring, and the communication delay of the spacecrafts is taken as 5 s. When solving the magnetic moment, considering the most energy saving, the energy balance, the decoupling of electromagnetic force and moment and the minimum external force required by the system, the value of the configured magnetic moment parameter is as follows:
W1i＝10-11×I3×3、W2i＝10-9×I3×3、γi＝102、Wo＝105×I3×3(ii) a Then simulation was performed with Matlab.
From simulation results, it can be seen that in the presence of position and velocity perturbation, the robust synovial membrane cooperative controller designed according to the method provided by the invention can realize the homing of the track within 700s by using electromagnetic interaction, and the position tracking error is 10-6Order of magnitude, the tracking error of the controller to the speed is 10-8And the method has higher precision. At the same time, the optimized magnetic moment distribution is 10 orders of magnitude5The magnetic moment can be realized with superconducting coils. The electromagnetic force required for control is in the order of mN. Simulation results show that the electromagnetic spacecraft formation robust cooperative controller designed by the invention canThe hovering task at any position of the spacecraft formation can be effectively realized, and the robustness to internal and external uncertainties existing in the system is strong.
Fig. 5 is a schematic overall structure diagram of an electromagnetic spacecraft formation hover cooperative control system according to an embodiment of the present invention, and as shown in fig. 5, based on any of the embodiments, an electromagnetic spacecraft formation hover cooperative control system is provided, including:
the electromagnetic force calculation module 1 is used for regarding an electromagnetic field generated by electromagnetic coils installed on any electromagnetic spacecraft as a dipole, establishing an electromagnetic force far field model, calculating the electromagnetic force between every two electromagnetic coils in the electromagnetic force far field model to obtain a first electromagnetic force calculation equation, and calculating the electromagnetic force borne by the electromagnetic spacecraft according to the first electromagnetic force calculation equation to obtain a second electromagnetic force calculation equation;
the control law design module 2 is used for establishing a reference coordinate system by taking the mass center of the reference spacecraft as a coordinate origin, taking a circular orbit of the elliptical orbit of the reference spacecraft, which moves in the same period, as a nominal orbit, establishing a target kinetic equation of relative motion of the electromagnetic spacecraft and the reference spacecraft on the basis of the nominal orbit under the reference coordinate system, and designing a robust control law by adopting a sliding mode control method on the basis of the target kinetic equation;
and the magnetic moment distribution module 3 is used for distributing the magnetic moments of all the electromagnetic spacecrafts according to the second electromagnetic force calculation equation and the robust control law.
Specifically, the invention provides an electromagnetic spacecraft formation hovering cooperative control system, which comprises an electromagnetic force calculation module 1, a control law design module 2 and a magnetic moment distribution module 3, and the method in any one of the method embodiments is realized through cooperation of the modules, and the specific implementation process can refer to the method embodiment, which is not described herein again.
According to the formation and hovering cooperative control system for the electromagnetic spacecrafts, for any electromagnetic spacecraft, an electromagnetic field generated by electromagnetic coils installed on the electromagnetic spacecrafts is regarded as a dipole, an electromagnetic force far-field model is established, the electromagnetic force between every two electromagnetic coils in the electromagnetic force far-field model is calculated, a first electromagnetic force calculation equation is obtained, the electromagnetic force borne by the electromagnetic spacecrafts is calculated according to the first electromagnetic force calculation equation, and a second electromagnetic force calculation equation is obtained; establishing a reference coordinate system by taking the mass center of a reference spacecraft as a coordinate origin, taking a circular orbit of the same period of an elliptical orbit of the motion of the reference spacecraft as a nominal orbit, establishing a target kinetic equation of the relative motion of the electromagnetic spacecraft and the reference spacecraft, and designing a robust control law by adopting a sliding mode control method based on the target kinetic equation; and distributing the magnetic moments of all the electromagnetic spacecrafts according to a second electromagnetic force calculation equation and a robust control law. The system designs robust cooperative control for the orbit hovering of the electromagnetic spacecraft formation system, so that the electromagnetic spacecraft formation hovering at any spatial position can be realized under the condition that the electromagnetic spacecraft cannot acquire real-time information of the reference orbit and is subjected to various interference effects, and the robustness is good. On the basis of the control, the optimized configuration of the magnetic moments of the formation of the electromagnetic spacecraft is realized by adopting an optimized method, and the magnetic moments obtained through the optimization are beneficial to decoupling of the orbit and the attitude of the electromagnetic spacecraft.
Fig. 6 shows a structural block diagram of an apparatus of an electromagnetic spacecraft formation hover cooperative control method according to an embodiment of the present invention. Referring to fig. 6, the apparatus of the electromagnetic spacecraft formation hover cooperative control method includes: a processor (processor)61, a memory (memory)62, and a bus 63; wherein, the processor 61 and the memory 62 complete the communication with each other through the bus 63; the processor 61 is configured to call program instructions in the memory 62 to perform the methods provided by the above-mentioned method embodiments, for example, including: regarding any electromagnetic spacecraft, regarding an electromagnetic field generated by electromagnetic coils installed on the electromagnetic spacecraft as a dipole, establishing an electromagnetic force far-field model, calculating the electromagnetic force between every two electromagnetic coils in the electromagnetic force far-field model to obtain a first electromagnetic force calculation equation, and calculating the electromagnetic force borne by the electromagnetic spacecraft according to the first electromagnetic force calculation equation to obtain a second electromagnetic force calculation equation; establishing a reference coordinate system by taking the mass center of a reference spacecraft as a coordinate origin, taking a circular orbit of the same period of an elliptical orbit of the motion of the reference spacecraft as a nominal orbit, establishing a target kinetic equation of the relative motion of the electromagnetic spacecraft and the reference spacecraft based on the nominal orbit under the reference coordinate system, and designing a robust control law by adopting a sliding mode control method based on the target kinetic equation; and distributing the magnetic moments of all the electromagnetic spacecrafts according to a second electromagnetic force calculation equation and a robust control law.
The present embodiment discloses a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, enable the computer to perform the method provided by the above-mentioned method embodiments, for example, comprising: regarding any electromagnetic spacecraft, regarding an electromagnetic field generated by electromagnetic coils installed on the electromagnetic spacecraft as a dipole, establishing an electromagnetic force far-field model, calculating the electromagnetic force between every two electromagnetic coils in the electromagnetic force far-field model to obtain a first electromagnetic force calculation equation, and calculating the electromagnetic force borne by the electromagnetic spacecraft according to the first electromagnetic force calculation equation to obtain a second electromagnetic force calculation equation; establishing a reference coordinate system by taking the mass center of a reference spacecraft as a coordinate origin, taking a circular orbit of the same period of an elliptical orbit of the motion of the reference spacecraft as a nominal orbit, establishing a target kinetic equation of the relative motion of the electromagnetic spacecraft and the reference spacecraft based on the nominal orbit under the reference coordinate system, and designing a robust control law by adopting a sliding mode control method based on the target kinetic equation; and distributing the magnetic moments of all the electromagnetic spacecrafts according to a second electromagnetic force calculation equation and a robust control law.
The present embodiments provide a non-transitory computer-readable storage medium storing computer instructions that cause the computer to perform the methods provided by the above method embodiments, for example, including: regarding any electromagnetic spacecraft, regarding an electromagnetic field generated by electromagnetic coils installed on the electromagnetic spacecraft as a dipole, establishing an electromagnetic force far-field model, calculating the electromagnetic force between every two electromagnetic coils in the electromagnetic force far-field model to obtain a first electromagnetic force calculation equation, and calculating the electromagnetic force borne by the electromagnetic spacecraft according to the first electromagnetic force calculation equation to obtain a second electromagnetic force calculation equation; establishing a reference coordinate system by taking the mass center of a reference spacecraft as a coordinate origin, taking a circular orbit of the same period of an elliptical orbit of the motion of the reference spacecraft as a nominal orbit, establishing a target kinetic equation of the relative motion of the electromagnetic spacecraft and the reference spacecraft based on the nominal orbit under the reference coordinate system, and designing a robust control law by adopting a sliding mode control method based on the target kinetic equation; and distributing the magnetic moments of all the electromagnetic spacecrafts according to a second electromagnetic force calculation equation and a robust control law.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above-described embodiments of the apparatus and the like of the electromagnetic spacecraft formation hovering cooperative control method are merely illustrative, where the units described as the separate components may or may not be physically separate, and the components displayed as the units may or may not be physical units, that is, may be located in one place, or may also be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
Finally, the method of the present application is only a preferred embodiment and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. An electromagnetic spacecraft formation hovering cooperative control method is characterized by comprising the following steps:
regarding any electromagnetic spacecraft, regarding an electromagnetic field generated by electromagnetic coils installed on the electromagnetic spacecraft as a dipole, establishing an electromagnetic force far-field model, calculating the electromagnetic force between every two electromagnetic coils in the electromagnetic force far-field model to obtain a first electromagnetic force calculation equation, and calculating the electromagnetic force applied to the electromagnetic spacecraft according to the first electromagnetic force calculation equation to obtain a second electromagnetic force calculation equation;
establishing a reference coordinate system by taking the mass center of a reference spacecraft as a coordinate origin, taking a circular orbit of the elliptical orbit of the reference spacecraft, which moves in the same period, as a nominal orbit, establishing a target kinetic equation of relative motion of the electromagnetic spacecraft and the reference spacecraft on the basis of the nominal orbit under the reference coordinate system, and designing a robust control law by adopting a sliding mode control method on the basis of the target kinetic equation;
and distributing the magnetic moments of all the electromagnetic spacecrafts according to the second electromagnetic force calculation equation and the robust control law.
2. The method according to claim 1, wherein the target kinetic equation for the relative motion of the electromagnetic spacecraft and the reference spacecraft based on the nominal orbit is established in the reference coordinate system by:
establishing a candidate kinetic equation of relative motion of the electromagnetic spacecraft and the reference spacecraft under the reference coordinate system;
and converting the candidate kinetic equation into the target kinetic equation according to the uncertainty by taking the deviation of the elliptical orbit relative to the nominal orbit, the perturbation of the earth's non-spherical gravity, the sunlight pressure, the error of the electromagnetic force far-field model and the gravity of other celestial bodies as uncertainty.
3. The method according to claim 1, wherein the robust control law is designed by adopting a sliding mode control method based on the target kinetic equation, and specifically comprises the following steps:
acquiring a sliding surface according to the current state and the nominal state of the electromagnetic spacecraft;
and selecting an arrival control law and an arrival condition, and designing the robust control law according to the arrival control law and the arrival condition on the basis of the sliding surface.
4. The method according to claim 1, wherein the robust control law is designed by adopting a sliding mode control method based on the target kinetic equation, and then the method further comprises the following steps:
and obtaining a cooperative item corresponding to the electromagnetic spacecraft according to the communication relation between the electromagnetic spacecraft and other electromagnetic spacecrafts, and adding the cooperative item to the robust control law to obtain a cooperative control law.
5. The method according to claim 4, wherein the obtaining of the corresponding synergy term of the electromagnetic spacecraft according to the communication relationship between the electromagnetic spacecraft and the other electromagnetic spacecraft is specifically:
taking each electromagnetic spacecraft as a node, taking the communication relation between every two electromagnetic spacecrafts as an edge, taking the communication performance between every two electromagnetic spacecrafts as an adjacency matrix, and establishing a weighted undirected graph;
and obtaining the corresponding cooperative item of the electromagnetic spacecraft according to the weighted undirected graph.
6. The method according to claim 1, wherein the magnetic moments of all the electromagnetic spacecraft are assigned according to the second electromagnetic force calculation equation and the robust control law, specifically:
for any electromagnetic spacecraft, substituting the robust control law into the second electromagnetic force calculation equation to obtain a constraint equation corresponding to the electromagnetic spacecraft;
setting an external force, and adding the external force to a constraint equation corresponding to one of all the electromagnetic spacecrafts;
and setting a target function based on the principles of energy optimization, magnetic moment configuration balance and orbit attitude decoupling, and distributing the magnetic moments of all the electromagnetic spacecrafts according to constraint equations corresponding to all the electromagnetic spacecrafts and the target function.
7. The method according to claim 6, wherein the objective function is specifically:
Figure FDA0002295630570000021
Figure FDA0002295630570000031
wherein u isiRepresenting the electromagnetic force suffered by the No. i spacecraft; w1i、W2iRepresenting a weight coefficient matrix; tau isiRepresenting the electromagnetic interference moment suffered by the spacecraft No. i; gamma rayiIs the selected trim factor; f. of0Represents an external force; wo is its trim coefficient matrix; n represents the total number of all spacecraft.
8. An electromagnetic spacecraft formation hovering cooperative control system, comprising:
the electromagnetic force calculation module is used for regarding an electromagnetic field generated by electromagnetic coils arranged on any electromagnetic spacecraft as a dipole, establishing an electromagnetic force far field model, calculating the electromagnetic force between every two electromagnetic coils in the electromagnetic force far field model to obtain a first electromagnetic force calculation equation, and calculating the electromagnetic force applied to the electromagnetic spacecraft according to the first electromagnetic force calculation equation to obtain a second electromagnetic force calculation equation;
the control law design module is used for establishing a reference coordinate system by taking the mass center of a reference spacecraft as a coordinate origin, taking a circular orbit of the same period of an elliptical orbit of the motion of the reference spacecraft as a nominal orbit, establishing a target kinetic equation of the relative motion of the electromagnetic spacecraft and the reference spacecraft on the basis of the nominal orbit under the reference coordinate system, and designing a robust control law by adopting a sliding mode control method on the basis of the target kinetic equation;
and the magnetic moment distribution module is used for distributing the magnetic moments of all the electromagnetic spacecrafts according to the second electromagnetic force calculation equation and the robust control law.
9. The equipment of the electromagnetic spacecraft formation hovering cooperative control method is characterized by comprising the following steps:
at least one processor; and
at least one memory communicatively coupled to the processor, wherein:
the memory stores program instructions executable by the processor, the processor invoking the program instructions to perform the method of any of claims 1 to 7.
10. A non-transitory computer-readable storage medium storing computer instructions that cause a computer to perform the method of any one of claims 1 to 7.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106094854A (en) * 2016-07-15 2016-11-09 中国人民解放军装备学院 Electromagnetism formation satellite attitude and track relation control method
CN106842951A (en) * 2017-03-08 2017-06-13 西安电子科技大学 Towards electrical property and the spatial networks antenna condition space modeling method for controlling
CN107065565A (en) * 2017-05-18 2017-08-18 中国人民解放军装备学院 A kind of Auto-disturbance-rejection Control pulled for cluster spacecraft electromagnetism

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105912020B (en) * 2016-05-26 2018-10-09 北京航空航天大学 A kind of Spacecraft Formation Flying method in weak stability boundaris region

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106094854A (en) * 2016-07-15 2016-11-09 中国人民解放军装备学院 Electromagnetism formation satellite attitude and track relation control method
CN106842951A (en) * 2017-03-08 2017-06-13 西安电子科技大学 Towards electrical property and the spatial networks antenna condition space modeling method for controlling
CN107065565A (en) * 2017-05-18 2017-08-18 中国人民解放军装备学院 A kind of Auto-disturbance-rejection Control pulled for cluster spacecraft electromagnetism

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
双电磁航天器编队构型保持自适应控制;徐增文 等;《北京航空航天大学学报》;20151231;第41卷(第12期);第2302-2308页 *
电磁航天器编队动力学建模与运动规划方法;邵龙飞;《北京航空航天大学学报》;20150430;第41卷(第4期);第737-743页 *

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