CN109765921B - Spacecraft formation cooperative control method capable of guaranteeing communication and avoiding collision - Google Patents

Spacecraft formation cooperative control method capable of guaranteeing communication and avoiding collision Download PDF

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CN109765921B
CN109765921B CN201910158643.1A CN201910158643A CN109765921B CN 109765921 B CN109765921 B CN 109765921B CN 201910158643 A CN201910158643 A CN 201910158643A CN 109765921 B CN109765921 B CN 109765921B
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胡庆雷
石永霞
董宏洋
郭雷
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Beihang University
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Abstract

The invention discloses a spacecraft formation cooperative control method for ensuring communication and avoiding collision, which comprises the following steps: under the condition of considering the existence of external interference, establishing a relative position dynamic model of a spacecraft formation flying system; describing the communication condition of the spacecraft formation flying system based on directed graph theory; defining a scalar potential function, and limiting a safe and reliable area for ensuring effective communication and avoiding collision of the spacecraft; and designing a self-adaptive cooperative controller to enable the final speeds of the spacecraft formation to be consistent. The method can ensure that the formation spacecraft can effectively communicate and avoid collision while realizing the consistency of the overall speed, has the advantages of strong anti-interference capability, strong robustness and the like, and is suitable for cooperative control of relative flying positions of the formation spacecraft.

Description

Spacecraft formation cooperative control method capable of guaranteeing communication and avoiding collision
Technical Field
The invention belongs to the technical field of spacecraft control, and particularly relates to a spacecraft formation cooperative control method for ensuring communication and avoiding collision, which is mainly applied to a spacecraft formation flying system with limited communication distance, limited safety distance, uncertain model and external interference.
Background
The spacecraft formation flying has more and more important functions in the field of modern aerospace due to the advantages of low relative cost, strong system robustness, high operation reliability, high task response speed and the like. When the space task is executed, wireless communication can be adopted among the formation spacecrafts in the spacecraft formation flying system to obtain the state information of the adjacent spacecrafts, and the controller is constructed by combining the state information of the controller, so that the cooperative control of the whole spacecraft formation flying system is realized.
However, when the formation space vehicles are relatively far apart, communication is often interrupted. Meanwhile, when the formation spacecraft are operated at a short distance, there is a risk of collision with each other. Therefore, it is particularly important to realize cooperative control under the constraint conditions of ensuring effective communication and avoiding collision of formation spacecraft. In addition, as the spacecraft formation mission is carried out, the uncertainty of a system model caused by the continuous consumption of fuel of the spacecraft and the interference of the system caused by the complex space operating environment can influence the normal operation of the spacecraft formation flight system to a certain extent, so that the spacecraft formation flight system is required to have the characteristics of strong robustness, strong anti-interference capability and the like. Therefore, the spacecraft formation flying system can keep the final speed consistent in a safe and reliable area under the conditions of model uncertainty and external interference, and is an important task for the cooperative control of the relative positions of spacecraft formation flying.
Disclosure of Invention
The technical problem of the invention is solved: aiming at the problems of limited communication distance, limited safety distance, uncertainty of a model, external interference and the like of a spacecraft formation flying system, a relative position self-adaptive cooperative control method which ensures communication and avoids collision is provided, the control method is strong in robustness and anti-interference capability and can enable the spacecraft formation flying system to operate in a safe and reliable area, the problems of the cooperative control of the communication distance, the safety distance and the relative position of the spacecraft formation flying system under the conditions of model uncertainty and external interference in the cooperative control process of the spacecraft formation flying system are solved, and the spacecraft formation flying system can efficiently and reliably complete a formation task.
According to an aspect of the invention, a spacecraft formation cooperative control method for ensuring communication and avoiding collision is provided, which comprises the following steps:
(1) under the condition of considering the existence of external interference, establishing a relative position dynamic model of a spacecraft formation flying system;
(2) describing the communication condition of the spacecraft formation flying system based on directed graph theory;
(3) defining a scalar potential function, and limiting a safe and reliable area for ensuring effective communication and avoiding collision of the spacecraft;
(4) and (3) designing a self-adaptive cooperative controller based on the dynamic model of the relative positions of the spacecraft formation flying systems established in the step (1), the communication conditions of the spacecraft formation flying systems in the step (2) and the scalar potential function defined in the step (3), so that the final speeds of the spacecraft formation tend to be consistent.
Further, the step (1) is specifically as follows:
considering the condition of external interference, the spacecraft formation flying system is assumed to comprise n spacecrafts; establishing an earth center inertial coordinate system (O-XYZ) by taking the earth center as an origin; setting a virtual spacecraft, and assuming that the virtual spacecraft operates at a true near point angle theta and a semi-major axis acEccentricity of ecAn elliptical orbit of (a); establishing an LVLH coordinate system (o-xyz) by taking the virtual spacecraft as a reference spacecraft; reference spacecraft relative to groundThe heart position is Rc＝[Rc,0,0]TThe superscript T denotes the matrix transposition, where RcRepresenting the distance of the virtual space vehicle from the earth's center in the direction of the x-axis
Figure GDA0002784789400000021
Calculating to obtain; establishing a relative position dynamic model of a spacecraft formation flying system by taking an LVLH coordinate system as a reference coordinate system as follows:
Figure GDA0002784789400000022
Figure GDA0002784789400000023
where ρ isi＝[ρix,ρiy,ρiz]TRepresenting the position of the ith spacecraft relative to the reference spacecraft, where pix，ρiy，ρizThe distances of the ith spacecraft relative to the reference spacecraft on the x axis, the y axis and the z axis are respectively; v. ofi＝[vix,viy,viz]TRepresenting the velocity of the ith spacecraft relative to the reference spacecraft, wherein vix，viy，vizThe speeds of the ith spacecraft relative to the reference spacecraft on the x axis, the y axis and the z axis respectively; m isiRepresenting the mass of the ith spacecraft; diRepresenting the external disturbance force suffered by the ith spacecraft; u. ofiControl signals representing the ith spacecraft;
Figure GDA0002784789400000024
representing the matrix of coriolis forces and centrifugal forces for the ith spacecraft, wherein,
Figure GDA0002784789400000025
to refer to the first derivative of the true anomaly theta of the spacecraft, as follows
Figure GDA0002784789400000031
Wherein the content of the first and second substances,
Figure GDA0002784789400000032
reflecting the average motion of the reference spacecraft; μ represents a gravitational constant;
Figure GDA0002784789400000033
the time-varying nonlinear term representing the ith spacecraft is as follows:
Figure GDA0002784789400000034
wherein the content of the first and second substances,
Figure GDA0002784789400000035
is the second derivative of the reference spacecraft true anomaly angle theta;
Figure GDA0002784789400000036
representing the distance of the ith spacecraft from the earth's center.
Further, the description of the communication situation of the spacecraft formation flight system in the step (2) specifically includes: wireless communication is assumed to be carried out among all spacecrafts in the formation flying system; the communication case is described as a weighted directed strong unicom graph G ═ { V, E, a }, where V ═ V1,…vi,…,vj,…,vnDenotes a set of nodes consisting of n formation spacecrafts, where v1,…vi,…,vj,…,vnRespectively represent 1 to n spacecraft nodes;
Figure GDA0002784789400000037
representing communication paths between formation spacecraft; a ═ aij]∈Rn×nRepresenting an adjacency matrix between the ith spacecraft and the jth spacecraft; if (v)i,vj) E denotes that communication can be established between spacecraft j and spacecraft i,the spacecraft j can obtain the information of the spacecraft i, and the element a in the adjacency matrixij> 0, wherein viAnd vjRespectively representing an ith spacecraft node and a jth spacecraft node; if it is not
Figure GDA0002784789400000038
The element a in the adjacency matrix indicates that the spacecraft j cannot obtain the information of the spacecraft iij0; meanwhile, considering that the spacecraft does not perform wireless communication per se, the element a in the adjacency matrixij0; directed strongly connected graph
Figure GDA0002784789400000039
The laplacian matrix of is L ═ Lij]∈Rn×nWherein l isij＝∑j≠iaij(i＝j)，lij＝-aij(i≠j)。
Further, in step (3), considering the communication distance limit and the safety distance limit, defining a scalar potential function between the spacecraft i and the spacecraft j as:
Figure GDA00027847894000000310
where ρ isaRepresents the maximum allowable distance between the spacecraft to ensure efficient communication; rhocRepresents the minimum allowable distance between the spacecraft to avoid collision; rhodIndicating a warning distance between the spacecraft to avoid collision. Scalar potential function V between spacecraft i and spacecraft jijAbout piThe gradient of (d) is:
Figure GDA00027847894000000311
wherein, delta1＝||ρi-ρj||4-2||ρi-ρj||2+ρa 2ρc 2+ρd 2ρa 2-ρd 2ρc 2；
Figure GDA0002784789400000041
ρiAnd ρjRespectively representing the position of the ith and jth spacecraft relative to the reference spacecraft.
Based on the scalar potential function defined above, when the ith spacecraft and the jth spacecraft are close to each other, if the distance between the two spacecraft approaches the minimum allowable distance for collision avoidance, the scalar potential function value between the two spacecraft will become very large. When spacecraft i and spacecraft j are far from each other, if the distance between the two is close to the maximum allowable distance for effective communication, the potential energy between the two spacecraft will be very large and correspondingly the scalar potential function will become very large. Therefore, the forbidden flight area of the spacecraft is limited by using a higher potential function value, and the spacecraft can be ensured to operate in a safe and reliable area with effective communication and collision avoidance.
Further, based on the dynamic model of the relative position of the spacecraft formation flying system under the condition of external interference, which is established in the step (1), the description of the communication condition of the spacecraft formation flying system in the step (2) and the scalar potential function defined in the step (3), considering the influence of model uncertainty and external interference, the adaptive cooperative controller is designed as follows:
Figure GDA0002784789400000042
the adaptive law is:
Figure GDA0002784789400000043
wherein the content of the first and second substances,
Figure GDA0002784789400000044
αicontrol gain is more than 0; epsilon > 0 is a normal number for compensating interference, and epsilon is more than or equal to | | | di||∞；ηiThe adjustable constant is more than 0, beta is more than 0 and is positive;
Figure GDA0002784789400000045
is an estimated value of the mass of the ith spacecraft; v. ofiAnd vjRespectively representing the speeds of the ith spacecraft and the jth spacecraft relative to the reference spacecraft; vijRepresenting a scalar potential function between spacecraft i and spacecraft j.
Compared with the prior art, the invention has the advantages that:
(1) according to the spacecraft formation cooperative control method capable of guaranteeing communication and avoiding collision, aiming at the constraints of limited communication distance, limited safety distance and the like of a spacecraft formation flying system, a cooperative controller is designed based on a scalar potential function, and the spacecraft formation flying system is guaranteed to operate in a safe and reliable area;
(2) the invention aims to design a cooperative controller based on a self-adaptive technology to perform anti-interference processing under the condition that model uncertainty and external interference exist in a task execution stage of a spacecraft formation flying system in a complex space environment, so that the robustness of the system is improved, and the space task is guaranteed to be efficiently and reliably completed.
Drawings
FIG. 1 is a flow chart of a spacecraft formation cooperative control method for ensuring communication and avoiding collision according to the present invention;
FIG. 2 is a schematic diagram of a spacecraft formation flight system;
FIG. 3 is a schematic view of an operating region of a spacecraft formation flight system;
fig. 4 is a schematic view of communication conditions of a spacecraft formation flight system, and the spacecraft formation flight system composed of three spacecraft is taken as an example.
Detailed Description
Reference will now be made in detail to the embodiments of the present invention, the following examples of which are intended to be illustrative only and are not to be construed as limiting the scope of the invention.
The spacecraft formation cooperative control method for ensuring communication and avoiding collision comprises the following steps: firstly, establishing a relative position dynamic model of a spacecraft formation flying system; then, based on directed graph theory, communication condition description is carried out on the spacecraft formation flying system; then, considering the limitation of communication distance and the limitation of safety distance, defining a scalar potential function; and finally, considering model uncertainty and external interference influence, and designing a cooperative controller based on a self-adaptive technology to make the final speeds of the formation spacecrafts tend to be consistent. The flow chart of the whole method is shown in fig. 1, and the specific implementation steps are as follows:
in the first step, assuming that the spacecraft formation flying system includes n number of spacecraft, the description will be made by taking fig. 2 as an example: establishing an earth center inertial coordinate system (O-XYZ) by taking the earth center as an origin; setting a virtual spacecraft, and assuming that the virtual spacecraft operates at a true near point angle of theta and half and a semimajor axis of acEccentricity of ecAn elliptical orbit of (a); establishing an LVLH coordinate system (o-xyz) by taking the virtual spacecraft as a reference spacecraft; the position of the reference spacecraft relative to the Earth's center is Rc＝[Rc,0,0]TThe superscript T denotes the matrix transpose, wherein,
Figure GDA0002784789400000051
Figure GDA0002784789400000052
representing the distance between the reference spacecraft and the geocenter in the direction of the x axis; establishing a relative position dynamic model of the spacecraft formation process by taking an LVLH coordinate system as a reference coordinate system:
Figure GDA0002784789400000053
Figure GDA0002784789400000054
where ρ isi＝[ρix,ρiy,ρiz]TRepresenting the ith spacecraft relative to the reference spacecraftPosition where pix，ρiy，ρizThe distances of the ith spacecraft relative to the reference spacecraft on the x axis, the y axis and the z axis are respectively; v. ofi＝[vix,viy,viz]TRepresenting the velocity of the ith spacecraft relative to the reference spacecraft, wherein vix，viy，vizThe speeds of the ith spacecraft relative to the reference spacecraft on the x axis, the y axis and the z axis respectively; m isiRepresenting the mass of the ith spacecraft; diRepresenting the external disturbance force suffered by the ith spacecraft; u. ofiControl signals representing the ith spacecraft;
Figure GDA0002784789400000055
representing the matrix of coriolis forces and centrifugal forces for the ith spacecraft, wherein,
Figure GDA0002784789400000056
the first derivative of the virtual navigator true anomaly angle θ is as follows:
Figure GDA0002784789400000061
wherein the content of the first and second substances,
Figure GDA0002784789400000062
reflecting the average motion of the reference spacecraft; μ represents a gravitational constant;
Figure GDA0002784789400000063
the time-varying nonlinear term representing the ith spacecraft is as follows:
Figure GDA0002784789400000064
wherein the content of the first and second substances,
Figure GDA0002784789400000065
to the second order of the true anomaly theta of the reference spacecraftA derivative;
Figure GDA0002784789400000066
representing the distance of the ith spacecraft from the earth's center.
According to the actual spacecraft formation flying system, considering a spacecraft formation flying system consisting of three spacecrafts with the mass of 20kg, m is1＝m2＝m320 kg; setting a reference spacecraft to run on an elliptical orbit, and selecting an orbit element as a semi-major axis ac7000kg, orbital eccentricity ec0.02, and 0rad is set for the initial value theta (0) of the true near point angle of the reference spacecraft; external interference d ═ 0.001[ sin (t), cos (t), sin (t)]TN; gravitational constant mu of 3.986 × 1014N·m2Per kg; the positions of three formation spacecrafts at the initial moment are (71,0,50) m, (0, -100,0) m, (-71,0, -50) m; the speeds of the three formation spacecrafts at the initial moment are respectively (0, -0.5,0) m/s, (-0.25,0, -0.25) m/s, (0, -0.5,0) m/s.
Secondly, describing the communication condition of the spacecraft formation flying system: wireless communication is carried out among all the spacecrafts in the spacecraft formation flying system; the communication case is described as weighted directed strong unicom graph G ═ V, E, a }, V ═ V1,…vi,…,vj,…,vnRepresents a set of nodes consisting of n formation spacecraft;
Figure GDA0002784789400000069
representing communication paths between formation spacecraft; a ═ aij]∈Rn×nRepresenting an adjacency matrix between the ith spacecraft and the jth spacecraft; if (v)i,vj) E represents that communication can be established between the spacecraft j and the spacecraft i, the spacecraft j can obtain the information of the spacecraft i, and an element a in the adjacency matrixij> 0, wherein viAnd vjRespectively representing an ith spacecraft node and a jth spacecraft node; if it is not
Figure GDA00027847894000000610
Information indicating that spacecraft j cannot obtain spacecraft i, adjacency matrixMiddle element aij0; meanwhile, considering that the spacecraft does not perform wireless communication per se, the element a in the adjacency matrixij0. Considering a spacecraft formation flying system consisting of three spacecrafts, the communication situation is shown in figure 4, a in an adjacent matrix12＝0.01，a23＝0.01，a310.01, and the rest elements are zero; this indicates that the second spacecraft can obtain information from the first spacecraft, the third spacecraft can obtain information from the second spacecraft, and the first spacecraft can obtain information from the third spacecraft. Directed strongly connected graph
Figure GDA0002784789400000067
The laplacian matrix of is L ═ Lij]∈Rn ×nWherein l isij＝∑j≠iaij(i＝j)，lij＝-aij(i ≠ j), as follows:
Figure GDA0002784789400000068
and thirdly, defining a scalar potential function, and constraining a spacecraft communication limited region and a collision avoidance region, wherein the scalar potential function between a spacecraft i and a spacecraft j is designed as follows:
Figure GDA0002784789400000071
where ρ isaRepresents the maximum allowable distance between the spacecraft to ensure effective communication, and is selected as 100 m; rhocRepresenting the minimum allowable collision avoidance distance between the spacecrafts, and selecting the minimum allowable collision avoidance distance as 10 m; rhodThe warning distance for avoiding collision between the spacecrafts is selected to be 15 m. The relationship between the three distances is shown in fig. 3. Scalar potential function V between spacecraft i and spacecraft jijAbout piThe gradient of (d) is:
Figure GDA0002784789400000072
wherein, delta1＝||ρi-ρj||4-2||ρi-ρj||2+ρa 2ρc 2+ρd 2ρa 2-ρd 2ρc 2；
Figure GDA0002784789400000075
ρiAnd ρjRespectively representing the position of the ith and jth spacecraft relative to the reference spacecraft.
Based on the scalar potential function defined above, when the ith spacecraft and the jth spacecraft are close to each other, if the distance between the two spacecraft approaches the minimum allowable distance for collision avoidance, the scalar potential function value between the two spacecraft will become very large. When spacecraft i and spacecraft j are far from each other, if the distance between the two is close to the maximum allowable distance for effective communication, the potential energy between the two spacecraft will be very large and correspondingly the scalar potential function will become very large. Therefore, the forbidden flight area of the spacecraft is limited by using a higher potential function value, and the spacecraft can be ensured to operate in a safe and reliable area with effective communication and collision avoidance.
Fourthly, based on the dynamic model of the relative position of the spacecraft formation flying system under the condition of external interference, which is established in the first step, and the scalar potential function defined in the communication condition description and the third step of the spacecraft formation flying system in the second step, model uncertainty and external interference are considered, and based on the self-adaptive technology, a cooperative controller is designed to be as follows:
Figure GDA0002784789400000073
the adaptive law is:
Figure GDA0002784789400000074
wherein the content of the first and second substances,
Figure GDA0002784789400000076
αithe gain is controlled when the value is more than 0, and the value is selected as alpha through adjusting parametersi0; epsilon > 0 is a normal number for compensating interference, and epsilon is more than or equal to | | | di||∞Selecting epsilon as 0.05 by regulating the parameters; etaiThe adjustable constant is more than 0, beta is more than 0 and is selected as eta by adjusting parametersi＝0.5，β＝0.01；
Figure GDA0002784789400000081
For the estimated value of the ith spacecraft quality, the initial values of the three formation spacecraft quality estimation are all selected as
Figure GDA0002784789400000082
Adaptive cooperative controller uiThe formation spacecraft can be ensured to be effectively communicated, and collision can not occur; meanwhile, the final speeds of the formation spacecrafts tend to be consistent, so that the whole spacecraft formation flight system can run in a safe and reliable area to realize the cooperative control of the relative positions under the action of model uncertainty and external interference.
By Matlab simulation, a spacecraft formation cooperative control method which ensures communication and avoids collision can be obtained, the final speeds of spacecraft formation flying systems can be consistent under the action of limited communication distance, limited safety distance, uncertain model and external interference, and the method has strong robustness and anti-interference capability and can ensure that the spacecraft formation flying systems operate in safe and reliable areas.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (1)

1. A spacecraft formation cooperative control method for ensuring communication and avoiding collision is characterized by comprising the following steps:
(1) under the condition of considering the existence of external interference, establishing a relative position dynamic model of a spacecraft formation flying system; the specific process is as follows:
under the condition that external interference exists, assuming that a spacecraft formation flying system comprises n spacecrafts, and establishing a geocentric inertial coordinate system O-XYZ by taking the geocentric as an origin; setting a virtual spacecraft, and assuming that the virtual spacecraft operates at a true near point angle theta and a semi-major axis acEccentricity of ecAn elliptical orbit of (a); establishing an LVLH coordinate system o-xyz by taking the virtual spacecraft as a reference spacecraft; the position of the reference spacecraft relative to the Earth's center is Rc＝[Rc，0，0]TThe superscript T denotes the matrix transposition,
Figure FDA0002784789390000011
representing the distance between the reference spacecraft and the geocenter in the direction of the x axis; establishing a relative position dynamic model of a spacecraft formation flying system by taking an LVLH coordinate system as a reference coordinate system as follows:
Figure FDA0002784789390000012
Figure FDA0002784789390000013
where ρ isi＝[ρix，ρiy，ρiz]TRepresenting the position, p, of the ith spacecraft relative to the reference spacecraftix，ρiy，ρizThe distances of the ith spacecraft relative to the reference spacecraft on the x axis, the y axis and the z axis are respectively; v. ofi＝[vix，viy，viz]TRepresenting the velocity of the ith spacecraft relative to the reference spacecraft, wherein vix，viy，vizThe speeds of the ith spacecraft relative to the reference spacecraft on the x axis, the y axis and the z axis respectively; m isiRepresenting the mass of the ith spacecraft; u. ofiControl signals representing the ith spacecraft; diRepresenting the external disturbance force suffered by the ith spacecraft;
Figure FDA0002784789390000014
representing the matrix of coriolis forces and centrifugal forces for the ith spacecraft, wherein,
Figure FDA0002784789390000015
wherein the content of the first and second substances,
Figure FDA0002784789390000016
reflecting the average motion of the reference spacecraft; μ represents a gravitational constant;
Figure FDA0002784789390000017
the time-varying nonlinear term representing the ith spacecraft is as follows:
Figure FDA0002784789390000018
wherein the content of the first and second substances,
Figure FDA0002784789390000019
is the second derivative of the reference spacecraft true anomaly angle theta;
Figure FDA00027847893900000110
representing the distance of the ith spacecraft relative to the geocentric;
(2) describing the communication condition of the spacecraft formation flying system based on directed graph theory; the specific process is as follows:
wireless communication is assumed to be carried out among all spacecrafts in the formation flying system; the communication case is described as a weighted directed strong unicom graph G ═ { V, E, a }, where V ═ V1，...vi，...，vj，...，vnDenotes a set of nodes consisting of n spacecraft, where v1，...vi，...，vj，...，vnRespectively represent 1 to n spacecraft nodes;
Figure FDA0002784789390000021
Figure FDA0002784789390000022
representing a set of communication paths between the formation spacecraft; if (v)i，vj) E represents that the communication can be established between the spacecraft j and the spacecraft i, the spacecraft j can obtain the information of the spacecraft i, and then the element a in the adjacency matrixijIs greater than 0; if it is not
Figure FDA0002784789390000026
The element a in the adjacency matrix indicates that the spacecraft j cannot obtain the information of the spacecraft iij0, wherein viAnd vjRespectively representing an ith spacecraft node and a jth spacecraft node; meanwhile, considering that the spacecraft does not perform wireless communication per se, the element a in the adjacency matrixij0; the laplacian matrix of the directed strong connectivity graph G is L ═ Lij]∈Rn×nWherein l isij＝∑j≠iaij，i＝j；lij＝-aij，i≠j；
(3) Defining a scalar potential function, and limiting a safe and reliable area for ensuring effective communication and avoiding collision of the spacecraft;
considering the communication distance constraint and the safety distance constraint, a scalar potential function between the spacecraft i and the spacecraft j is defined as:
Figure FDA0002784789390000023
where ρ isaRepresents the maximum allowable distance between the spacecraft to ensure efficient communication; rhocRepresents the minimum allowable distance between the spacecraft to avoid collision; rhodRepresenting a warning distance between the spacecraft to avoid collision, a scalar potential function V between spacecraft i and spacecraft jijAbout piThe gradient of (d) is:
Figure FDA0002784789390000024
wherein, delta1＝||ρi-ρj||4-2||ρi-ρj||2+ρa 2ρc 2+ρd 2ρa 2-ρd 2ρc 2；
Figure FDA0002784789390000025
ρjRepresenting the position of the jth spacecraft relative to the reference spacecraft;
(4) designing a self-adaptive cooperative controller based on the dynamic model of the relative positions of the spacecraft formation flying systems established in the step (1), the communication conditions of the spacecraft formation flying systems in the step (2) and the scalar potential function defined in the step (3), so that the final speeds of the spacecraft formation tend to be consistent;
designing the self-adaptive cooperative controller as follows:
Figure FDA0002784789390000031
adaptive law:
Figure FDA0002784789390000032
wherein alpha isiControl gain is more than 0; n is the number of the spacecrafts in the spacecraft formation flying system; a ═ aij]∈Rn×nRepresenting an adjacency matrix between the ith spacecraft and the jth spacecraft; v. ofiAnd vjRespectively representing the speeds of the ith spacecraft and the jth spacecraft relative to the reference spacecraft; epsilon > 0 is a normal number for compensating interference, and epsilon is more than or equal to | | | di||∞；ηiThe adjustable constant is more than 0, beta is more than 0 and is positive;
Figure FDA0002784789390000033
is an estimated value of the mass of the ith spacecraft;
Figure FDA0002784789390000034
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