CN111026154A - Six-degree-of-freedom cooperative control method for preventing collision in spacecraft formation - Google Patents

Six-degree-of-freedom cooperative control method for preventing collision in spacecraft formation Download PDF

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CN111026154A
CN111026154A CN201911259037.5A CN201911259037A CN111026154A CN 111026154 A CN111026154 A CN 111026154A CN 201911259037 A CN201911259037 A CN 201911259037A CN 111026154 A CN111026154 A CN 111026154A
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spacecraft
degree
slave
determining
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黄静
孙俊
朱东方
孙禄君
孙杰
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Shanghai Aerospace Control Technology Institute
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • 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 discloses a six-degree-of-freedom cooperative control method for preventing collision in spacecraft formation, which comprises the following steps: s1, determining a complete mathematical model of six-degree-of-freedom motion of the master-slave formation of the spacecraft, and converting the dynamic model of the relative position into a dynamic model related to the distance between the spacecraft; s2, determining a preset performance function of six degrees of freedom for collision avoidance of spacecraft formation, performing error model conversion, and determining a six-degree-of-freedom cooperative robust control law of a sliding mode variable structure. The sliding mode variable structure control technology and the preset performance control are combined, the controller design utilizes the advantages of the preset performance function, the transient and steady performance of the system are considered, and the collision avoidance requirement of the system is met; the sliding mode variable structure control ensures that the system has certain robust interference suppression performance under the action of external interference; the six-degree-of-freedom high-precision cooperative control of the relative attitude and the relative position of the spacecraft with the external interference and the collision avoidance constraint is considered.

Description

Six-degree-of-freedom cooperative control method for preventing collision in spacecraft formation
Technical Field
The invention belongs to the technical field of nonlinear control system robust control, and relates to a six-degree-of-freedom cooperative control method for spacecraft formation.
Background
Spacecraft formation flying has become a hot point of recent research in the field of aerospace control due to the advantages of flexible structure, powerful function, high reliability, long life cycle, low emission risk and the like. In the process of formation of the spacecraft, a plurality of spacecrafts form a specific formation configuration, and space tasks are completed in a manner similar to a virtual single spacecraft through inter-satellite information interaction, interaction and cooperative work. When the whole formation system executes some complex formation tasks, such as a deep space interferometer, a synthetic aperture radar and the like, each spacecraft in the formation is required to meet the orbit and attitude requirements (absolute expected attitude and orbit) of the whole formation, and meanwhile, the relative attitude and relative position between each spacecraft are required to meet certain constraints and meet specified consistency requirements (such as constant configuration, consistent attitude, beam synchronization and the like), so that the problem of cooperative control of a distributed system is involved.
The challenge in flying formation of spacecraft as compared to single spacecraft missions is to maintain precise attitude coordination while maintaining a fixed relative spacecraft distance. On one hand, when the formation configuration of the spacecraft is established and maintained, a control strategy needs to be adopted to avoid collision between the spacecrafts. On the other hand, while maintaining the formation reconstruction, it is necessary to obtain high relative position and relative pose accuracy.
When the configuration control of the near-earth orbit ultra-compact spacecraft is carried out under the constraint conditions of external interference and collision avoidance, the six-degree-of-freedom coordination control of spacecraft formation needs to be considered.
At present, the problem of spacecraft formation configuration control under the constraint conditions of external interference and collision avoidance is considered, most of spacecraft formation configuration control only considers relative position control, and the transient state performance and the steady state performance of a system are hardly considered in the design process of a controller aiming at the problem of six-degree-of-freedom cooperative control.
Disclosure of Invention
The invention aims to solve the problems in the prior art, and provides an anti-collision six-degree-of-freedom cooperative control algorithm for spacecraft formation, which is used for realizing six-degree-of-freedom high-precision cooperative control of relative postures and relative positions of spacecraft formation based on a preset performance control and sliding mode variable structure control method under the constraint conditions of external interference and anti-collision.
The Preset Performance Control (PPC) is one of the research hotspots in the current control community, and has the advantage that the transient and steady-state performance of the system can be considered simultaneously on the basic premise of ensuring the stability of the system. The method can pre-design the convergence trajectory boundary of the state quantity, and the boundary constraint can be subjected to unconstrained processing through a nonlinear mapping function. The invention combines the preset performance control method with the sliding mode control method, provides a design method of the nonlinear system preset performance controller aiming at a strict feedback nonlinear system with external disturbance, such as spacecraft formation, and designs the convergence track boundary of each cooperative state quantity according to task requirements, thereby ensuring that the transient and steady-state performance of the system meets the preset requirement and ensuring that the system has certain robust interference suppression performance.
In order to achieve the above object, the technical solution of the present invention is: a six-degree-of-freedom cooperative control algorithm for collision avoidance of spacecraft formation comprises the following steps:
(1) determining a six-degree-of-freedom mathematical model of relative attitude and relative position of spacecraft formation;
(2) converting a relative motion mathematical model of the formation spacecraft, and converting a relative position dynamic model into a dynamic model related to the distance between the spacecraft before designing a controller in order to ensure that a system meets the state constraint requirement of collision prevention;
(3) determining a collision prevention six-degree-of-freedom preset performance function for spacecraft formation and performing error model conversion;
(4) and determining a six-degree-of-freedom cooperative robust control law of the sliding mode variable structure, so that the closed-loop system is asymptotically stable, and the six-degree-of-freedom cooperative control for preventing collision of spacecraft formation under the interference condition is realized.
In the step (1), without loss of generality, the following assumptions are made:
1) the mass and the rotational inertia of the slave spacecraft during the flight are kept unchanged;
2) the main spacecraft is ideally controlled, namely the orbit control force is supposed to just counteract the action of the external interference force;
3) the main spacecraft runs along a perfect circle orbit;
4) the relative distance between the master satellite (master spacecraft) and the slave satellite (slave spacecraft) is less than 50 km;
5) the disturbance forces and disturbance moment vectors experienced by the slave satellites (slave spacecraft) are bounded.
The method comprises the following specific steps:
firstly, determining a mathematical model of the relative position of a master-slave spacecraft formation according to the assumed conditions and the dynamic principle as formula (1)
Figure BDA0002311093870000031
Wherein R isrAs a relative position vector of the slave spacecraft with respect to the master spacecraft,
Figure BDA0002311093870000032
Rlis the position vector of the main spacecraft in the ECI; x, y and z respectively represent relative position vectors RrProjection on three axes of a main spacecraft reference system; m isfRepresenting the mass of the slave spacecraft; dffRepresenting external force disturbances acting on the slave spacecraft; ffRepresenting the control forces acting on the slave spacecraft; omegaoRepresents the orbital angular velocity of the main spacecraft and μ is the gravitational constant. Coriolis matrix Ct(ωo) Is defined as
Figure BDA0002311093870000033
Non-linear term Nt(Rr,ωo,Rl) Is composed of
Figure BDA0002311093870000034
In the formula rlIs the orbit height of the main spacecraft.
Second, defining q according to the assumed conditions and dynamics principleslAnd q isfDefining omega for the attitude quaternion of the master (master spacecraft) and the slave (slave spacecraft) respectivelylAnd ωfThe attitude angular velocities of the master (master) and slave spacecraft, respectively, under the inertial system. Defining a relative attitude quaternion qr＝[ηrεr]TRepresenting the attitude deviation from the main spacecraft body coordinate system to the slave spacecraft body coordinate system, and the relative attitude angular velocity omegarRepresenting the projection of the angular velocity of the slave spacecraft relative to the master spacecraft in the slave spacecraft body coordinate system. Determining the relative attitude quaternion and the relative attitude angular velocity as
Figure BDA0002311093870000035
Figure BDA0002311093870000036
Wherein
Figure BDA0002311093870000037
Representing quaternion multiplication, C being a rotation matrix described by quaternion
C＝(ηr 2-εr Tεr)I3+2εrεr T+2ηrS(εr) (5)
For any vector χ ═ χ1χ2χ3]T∈R3The symbol S (χ) represents a skew symmetric matrix
Figure BDA0002311093870000041
The kinematic model for determining the relative attitude of the master-slave spacecraft is the formula (6)
Figure BDA0002311093870000042
Wherein the content of the first and second substances,
Figure BDA0002311093870000043
the dynamic model for determining the relative attitude of the master-slave spacecraft formation is formula (7)
Figure BDA0002311093870000044
Wherein, Λr＝S(Cωl)Jf+JfS(Cωl)-S(Jfωf)，
Figure BDA0002311093870000045
Wherein JlAnd JfThe moment of inertia, u, of the master and slave spacecraft, respectivelyfIndicating the control moment, d, acting on the slave spacecraftufIs the disturbing moment received from the spacecraft.
The kinematic equation (6) of the relative attitude of the formation spacecraft and the kinetic equation (7) of the relative attitude form a complete mathematical model of the six-degree-of-freedom motion of the master-slave formation.
In the step (2), because the preset performance function directly acts on the state variable, the transient state performance and the steady state performance of the system are ensured to meet the preset requirements by designing the convergence trajectory boundary. In order to ensure that the system meets the state constraint requirements for collision avoidance, the invention converts the relative position state variables into quantities related to the distance L between the spacecraft prior to controller design. Here, the dynamics with respect to z in the motive dynamics equation (8) are selected to be rewritten as the dynamics equation with respect to L, according to which
Figure BDA0002311093870000046
Defining new vectors
Figure DEST_PATH_FDA0002311093860000032
Determining a new relative position kinetic model
Figure BDA0002311093870000048
Wherein N isL(Rr,ω,Rl,RL)＝[NL1NL2NL3]T，
Figure BDA0002311093870000049
Figure BDA0002311093870000051
Figure BDA0002311093870000052
Figure BDA0002311093870000053
In the step (3), determining a spacecraft formation collision avoidance six-degree-of-freedom control system model and a preset performance function and performing error model conversion, the specific steps are as follows:
first step, define
Figure BDA0002311093870000054
Six-degree-of-freedom control model for determining formation spacecraft
Figure BDA0002311093870000055
Wherein the content of the first and second substances,
Figure BDA0002311093870000056
Figure BDA0002311093870000057
secondly, determining a preset performance function as shown in the formula (11)
Figure BDA0002311093870000058
Where ρ isi0、ρi∞、liIs a preset normal number. Rhoi0The initial value of the preset performance function is selected, and the initial value is required to be greater than the norm of the state quantity; rhoi∞The final value of the performance function is preset, and the final convergence of the state quantity in a stable region rho can be ensuredi∞In the selection, the selection is required to be selected according to the precision requirement of the actual engineering (the smaller is not the better, the too high precision requirement can cause too large control input), liFor the error convergence rate, it can be ensured that the system state converges at least at an exponential rate, and the execution capacity of the actual system should be considered when selecting.
Definition of
Figure BDA0002311093870000059
Wherein x isdIs x1Desired terminal state of e1＝[e11… e16]T∈R6×1.e2＝[e21… e26]T∈R6×1Further considering the overshoot problem, the following preset performance bounds can be determined by using the preset performance function defined by equation (11):
Figure BDA0002311093870000061
β thereini∈[0,1]Are design parameters.
Thirdly, carrying out error model conversion, and introducing error transformation in the following form:
e1i(t)＝ρi(t)Ni(zi),i＝1,…,6 (14)
wherein z isiIs the new conversion error. N is a radical ofi(zi) Is a smooth and reversible function with strict increment and satisfies
Figure BDA0002311093870000062
Can equivalently transform the formula (14) into
Figure BDA0002311093870000063
Determining Ni(zi)：
Figure BDA0002311093870000064
Can find out
Figure BDA0002311093870000065
Figure BDA0002311093870000066
Determining an equivalent system model of the original system (10)
Figure BDA0002311093870000067
Wherein, z is defined as ═ z1,...,z6]T，
Figure BDA0002311093870000068
Figure BDA0002311093870000069
In the step (4), the six-degree-of-freedom cooperative robust controller of the sliding mode variable structure is determined, so that a closed-loop system is asymptotically stable, and the six-degree-of-freedom cooperative control for collision prevention of spacecraft formation under the interference condition is realized.
Consider an equivalent system model (19)
Defining a slip form face of
s＝x2+αz (20)
Then a six-degree-of-freedom cooperative controller based on sliding mode variable structure control can be determined
u＝-g-1[f(x1,x2)+α(-rv+rΛ(x1)x2)+kss+Dsgn(s)](21)
Wherein, α, ksMore than 0 is sliding mode gain, and the gain D is diag (D)1,D2,D3,D4,D5,D6) And has Di＝sup(|di|),i＝1,2,3。
In order to reduce the buffeting phenomenon essentially generated by the sign term sgn(s) in the sliding mode variable structure control, when the control is actually implemented, the sign term sgn(s) is replaced by an approximate hyperbolic tangent function.
The invention finally realizes the six-degree-of-freedom high-precision cooperative control of the relative attitude and the relative position of the spacecraft under the constraint conditions of external interference and collision avoidance.
Compared with the prior art, the invention has the following beneficial effects:
1) the control method provided gives consideration to the transient and steady-state performances of the system, namely ensures that the steady-state error of the system converges to a preset designated area and simultaneously ensures that the system has certain robust interference suppression performance under the action of external interference.
2) The anti-collision six-freedom-degree formation cooperative controller not only meets the high-precision control requirement of six-freedom-degree formation cooperation, but also takes the actual anti-collision engineering requirement into consideration, converts the relative position dynamic model into a distance-related mathematical model according to the state constraint variable, and is designed on the basis. The designed controller ensures the stability of the system, meets the control requirement and has potential application prospect.
Drawings
Fig. 1 is a block diagram of a satellite attitude control system according to an embodiment of the present invention.
Fig. 2 is a relative position change curve.
Fig. 3 is a relative velocity profile.
Fig. 4 is a relative attitude quaternion curve.
Fig. 5 is a relative attitude angular velocity change curve.
Detailed Description
The invention can be used for a six-degree-of-freedom cooperative control system for spacecraft formation. The invention mainly solves the problem of six-degree-of-freedom high-precision cooperative control of relative attitude and relative position of spacecraft formation under the constraint conditions of external interference and collision avoidance.
The present invention will be described in further detail with reference to the accompanying drawings.
Step S1, six-degree-of-freedom mathematical model of relative attitude and relative position of spacecraft formation
Considering the six-degree-of-freedom mathematical model of relative attitude and relative position of formation of spacecraft shown in fig. 1, without loss of generality, the following assumptions are made:
1) the mass and the rotational inertia of the slave spacecraft during the flight are kept unchanged;
2) the main spacecraft is ideally controlled, namely the orbit control force is supposed to just counteract the action of the external interference force;
3) the main spacecraft runs along a perfect circle orbit;
4) the relative distance between the master satellite and the slave satellite is less than 50 km;
5) the disturbance force and disturbance moment vectors experienced from the star are bounded.
The method comprises the following specific steps:
step S1.1, determining a mathematical model of the relative position of the master-slave spacecraft formation according to the assumed conditions and the dynamic principle as formula (1)
Figure BDA0002311093870000081
Wherein R isrAs a relative position vector of the slave spacecraft with respect to the master spacecraft,
Figure BDA0002311093870000082
Rlis the position vector of the main spacecraft in the ECI; x, y and z respectively represent relative position vectors RrProjection on three axes of a main spacecraft reference system; m isfRepresenting the mass of the slave spacecraft; dffRepresenting external disturbances acting on the slave spacecraft；FfRepresenting the control forces acting on the slave spacecraft; omegaoRepresents the orbital angular velocity of the main spacecraft and μ is the gravitational constant. Coriolis matrix Ct(ωo) Is defined as
Figure BDA0002311093870000083
Non-linear term Nt(Rr,ωo,Rl) Is composed of
Figure BDA0002311093870000091
Wherein r islIs the orbit height of the main spacecraft.
Step S1.2, defining q according to assumed conditions and dynamics principlelAnd q isfDefining omega as attitude quaternions of the main star and the sub-star respectivelylAnd ωfThe attitude angular velocities of the main star and the sub-star under the inertial system are respectively. Defining a relative attitude quaternion qr＝[ηrεr]TRepresenting the attitude deviation from the main spacecraft body coordinate system to the slave spacecraft body coordinate system, and the relative attitude angular velocity omegarRepresenting the projection of the angular velocity of the slave spacecraft relative to the master spacecraft in the slave spacecraft body coordinate system, ηrIs the scalar part of a quaternion. Determining the relative attitude quaternion and the relative attitude angular velocity as follows:
Figure BDA0002311093870000092
Figure BDA0002311093870000093
wherein the content of the first and second substances,
Figure BDA0002311093870000094
representing quaternion multiplication, C being a rotation matrix described by quaternion
C＝(ηr 2-εr Tεr)I3+2εrεr T+2ηrS(εr) (5)
For any vector χ ═ χ1χ2χ3]T∈R3The symbol S (χ) represents a skew symmetric matrix
Figure BDA0002311093870000095
The kinematic model for determining the relative attitude of the master-slave spacecraft is the formula (6)
Figure BDA0002311093870000096
Wherein the content of the first and second substances,
Figure BDA0002311093870000097
the dynamic model for determining the relative attitude of the master-slave spacecraft is a formula (7)
Figure BDA0002311093870000098
Wherein, Λr＝S(Cωl)Jf+JfS(Cωl)-S(Jfωf)，
Figure BDA0002311093870000101
JlAnd JfThe moment of inertia, u, of the master and slave spacecraft, respectivelyfRepresenting the control moment acting on the slave spacecraft, dufIs the disturbing moment received from the spacecraft.
The kinematic equation (6) of the relative attitude of the formation spacecraft and the kinetic equation (7) of the relative attitude form a complete mathematical model of the six-degree-of-freedom motion of the master-slave formation.
And S1.3, converting a relative motion mathematical model of the formation spacecraft, wherein in order to ensure that the system meets the state constraint requirement of collision prevention, a relative position kinetic model is required to be converted into a kinetic model related to the distance between the spacecraft before the controller is designed, and as the relative motion mathematical model of the formation spacecraft shown in the figure 1 is converted, because a preset performance function directly acts on a state variable, the transient state and the steady state performance of the system are ensured to meet the preset requirement by designing a convergence track boundary. In order to ensure that the system meets the state constraint requirements for collision avoidance, the relative position state variables need to be converted to quantities related to the distance L between the spacecraft prior to controller design. Here, the dynamics with respect to z in the motive dynamics equation (8) are selected to be rewritten as the dynamics equation with respect to L, according to which
Figure BDA0002311093870000102
Defining new vectors
Figure BDA0002311093870000103
Determining a new relative position kinetic model
Figure BDA0002311093870000104
Wherein N isL(Rr,ω,Rl,RL)＝[NL1NL2NL3]T，
Figure BDA0002311093870000105
Figure BDA0002311093870000106
Figure BDA0002311093870000107
Figure BDA0002311093870000108
And step S2, determining the conversion between the spacecraft formation anti-collision six-degree-of-freedom control system model and the preset performance error model. The conversion of the preset performance error model shown in fig. 1 specifically includes the following steps:
s2.1, definition
Figure BDA0002311093870000111
Six-degree-of-freedom control model for determining formation spacecraft
Figure BDA0002311093870000112
Wherein the content of the first and second substances,
Figure BDA0002311093870000113
Figure BDA0002311093870000114
s2.2, determining a preset performance function as shown in a formula (11)
Figure BDA0002311093870000115
Where ρ isi0、ρi∞、liIs a preset normal number. Rhoi0The initial value of the preset performance function is selected, and the initial value is required to be greater than the norm of the state quantity; rhoi∞The final value of the performance function is preset, and the final convergence of the state quantity in a stable region rho can be ensuredi∞In the selection, the selection is required to be selected according to the precision requirement of the actual engineeringiFor the error convergence rate, it can be ensured that the system state converges at least at an exponential rate, and the execution capacity of the actual system should be considered when selecting.
Definition of
Figure BDA0002311093870000116
Wherein x isdIs x1Desired terminal state of e1＝[e11… e16]T∈R6×1.e2＝[e21… e26]T∈R6×1Further considering the overshoot problem, the following preset performance bounds can be determined by using the preset performance function defined by equation (11):
Figure BDA0002311093870000117
β thereini∈[0,1]Are design parameters.
S2.3, performing error model conversion, and introducing error transformation in the following form:
e1i(t)＝ρi(t)Ni(zi),i＝1,…,6 (14)
wherein z isiIs the new conversion error. N is a radical ofi(zi) Is a smooth and reversible function with strict increment and satisfies
Figure BDA0002311093870000121
Can equivalently transform the formula (14) into
Figure BDA0002311093870000122
Determining Ni(zi)：
Figure BDA0002311093870000123
Can find out
Figure BDA0002311093870000124
Figure BDA0002311093870000125
Determining an equivalent system model of a six degree of freedom control model (10)
Figure BDA0002311093870000126
Wherein, z is defined as ═ z1,...,z6]T，
Figure BDA0002311093870000127
Figure BDA0002311093870000128
And S2.4, determining the sliding mode variable structure six-degree-of-freedom cooperative robust controller, so that the closed-loop system is asymptotically stable, and realizing the six-degree-of-freedom cooperative control for preventing collision of the spacecraft formation under the interference condition. The six-degree-of-freedom cooperative robust controller shown in FIG. 1 considers an equivalent system model (19)
Defining a slip form face of
s＝x2+αz (20)
Then a six-degree-of-freedom cooperative controller based on sliding mode variable structure control can be determined
u＝-g-1[f(x1,x2)+α(-rv+rΛ(x1)x2)+kss+Dsgn(s)](21)
Wherein, α, ksMore than 0 is sliding mode gain, and the gain D is diag (D)1,D2,D3,D4,D5,D6) And has Di＝sup(|di|),i＝1,2,3。
In order to reduce the buffeting phenomenon essentially generated by the sign term sgn(s) in the sliding mode variable structure control, when the control is actually implemented, the sign term sgn(s) is replaced by an approximate hyperbolic tangent function.
The invention finally realizes the six-degree-of-freedom high-precision cooperative control of the relative attitude and the relative position of the spacecraft under the constraint conditions of external interference and collision avoidance.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
The effectiveness of the implementation is illustrated in the following by a practical case simulation. And a certain master-slave spacecraft formation is used as a controlled object, and the control algorithm of the invention is adopted to verify the effectiveness of the self-adaptive cooperative control algorithm.
The mass of the master satellite and the mass of the slave satellite are both 120kg, and the inertia matrixes of the spacecraft of the master satellite and the slave satellite are both
Figure BDA0002311093870000131
The initial state of the main spacecraft attitude is
Figure BDA0002311093870000132
From the initial state of spacecraft attitude to
Figure BDA0002311093870000133
The initial value of the relative position is Rr(0)＝[22 28 -15]Tm,vr(0)＝[0 0 0]Tm/s, the sunlight pressure and moment, the aerodynamic force and moment, the residual magnetism interference moment and the like are considered, and the following parameters are adopted for setting:
ρ10＝0.5,ρ20＝0.6,ρ30＝0.8,ρ40＝22,ρ50＝30,ρ60＝17,ρi∞＝10-3,i＝1,2,3,4,5,6
li＝0.01(i＝1,2,3),li＝0.0167(i＝4,5,6),
Figure BDA0002311093870000134
M i＝-1(i＝1,2,3,4,5,6)
the simulation results are shown in fig. 2 to 5: fig. 2 to 5 show time response curves of the relative position, the relative velocity, the relative attitude quaternion and the relative attitude angular velocity of the spacecraft formation based on the six-degree-of-freedom high-precision cooperative control. As can be seen from the figure, the controller can achieve six-degree-of-freedom high-precision cooperative control of spacecraft formation, and the proposed six-degree-of-freedom cooperative control algorithm for preventing collision of spacecraft formation is effective.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (5)

1. A six-degree-of-freedom cooperative control method for preventing collision in spacecraft formation is characterized by comprising the following steps of:
s1, determining a complete mathematical model of the spacecraft master-slave formation six-degree-of-freedom motion, which comprises the following steps: a relative position kinematics model and a relative attitude dynamics model of the formation spacecraft; converting the relative position dynamic model into a dynamic model related to the distance between the spacecrafts;
s2, determining a preset performance function of collision prevention and avoidance of spacecraft formation, performing error model conversion, and further determining a six-degree-of-freedom cooperative robust control law of a sliding mode variable structure to realize the six-degree-of-freedom cooperative control of collision prevention and avoidance of spacecraft formation under the interference condition.
2. The six-degree-of-freedom cooperative control method for preventing collision in spacecraft formation according to claim 1, wherein in the step S1, the following conditions are assumed:
1) the mass and the rotational inertia of the slave spacecraft during the flight are kept unchanged;
2) the main spacecraft carries out ideal control: assuming that the track control force just counteracts the effect of the extraneous disturbance force;
3) the main spacecraft runs along a perfect circle orbit;
4) the relative distance between the master spacecraft and the slave spacecraft is less than 50 km;
5) the disturbance forces and disturbance moment vectors experienced from the spacecraft are bounded.
3. The six-degree-of-freedom cooperative control method for spacecraft formation collision avoidance according to claim 2, wherein the step S1 comprises:
step S1.1, determining a mathematical model of the relative position of the master-slave spacecraft formation according to the assumed conditions and the dynamics principle as formula (1)
Figure FDA0002311093860000011
Wherein R isrAs a relative position vector of the slave spacecraft with respect to the master spacecraft,
Figure FDA0002311093860000012
Rlis the position vector of the main spacecraft in the ECI; x, y and z respectively represent relative position vectors RrProjection on three axes of a main spacecraft reference system; m isfRepresenting the mass of the slave spacecraft; dffRepresenting external force disturbances acting on the slave spacecraft; ffRepresenting the control forces acting on the slave spacecraft; omegaoRepresents the orbital angular velocity of the main spacecraft, and mu is a gravity constant; coriolis matrix Ct(ωo) Is defined as:
Figure FDA0002311093860000013
non-linear term Nt(Rr，ωo，Rl) Comprises the following steps:
Figure FDA0002311093860000021
wherein r islIs the orbit height of the primary spacecraft;
step S1.2, defining q according to the assumed conditions and the dynamic principlelAnd q isfDefining omega for attitude quaternion of the master spacecraft and the slave spacecraft respectivelylAnd ωfThe attitude angular velocities of the main spacecraft and the slave spacecraft under an inertial system are respectively; defining a relative attitude quaternion qr＝[ηrεr]TRepresenting the attitude deviation from the main spacecraft body coordinate system to the slave spacecraft body coordinate system, and the relative attitude angular velocity omegarRepresenting the projection of the angular velocity of the slave spacecraft relative to the master spacecraft in a slave spacecraft body coordinate system; determining relative attitude quaternion qrAnd relative attitude angular velocity ωrRespectively as follows:
Figure FDA0002311093860000022
Figure FDA0002311093860000023
wherein the content of the first and second substances,
Figure FDA0002311093860000024
representing quaternion multiplication, C being a rotation matrix described by quaternion
C＝(ηr 2-εr Tεr)I3+2εrεr T-2ηrS(εr) (5)
For any vector χ ═ χ1χ2χ3]T∈R3The symbol S (χ) represents the following oblique symmetric matrix:
Figure FDA0002311093860000025
the kinematic model for determining the relative attitude of the master-slave spacecraft is shown as formula (6):
Figure FDA0002311093860000026
wherein the content of the first and second substances,
Figure FDA0002311093860000027
the dynamic model for determining the relative attitude of the master-slave spacecraft is a formula (7)
Figure FDA0002311093860000028
In the formula, Λr＝S(Cωl)Jf+JfS(Cωl)-S(Jfωf)，
Figure FDA0002311093860000029
JlAnd JfThe moment of inertia, u, of the master and slave spacecraft, respectivelyfRepresenting the control moment acting on the slave spacecraft, dufDisturbance moment received from the spacecraft; the kinematic equation (6) and the relative attitude kinetic equation (7) of the relative attitude of the master-slave spacecraft form a complete mathematical model of six-degree-of-freedom motion of the master-slave spacecraft;
s1.3, converting the relative position state variable into a quantity related to the distance L between the spacecrafts;
the dynamic equation regarding z in the dynamic equation (1) of the relative position is selected to be rewritten as the dynamic equation regarding L:
Figure FDA0002311093860000031
defining new vectors
Figure FDA0002311093860000032
Kinetic model to determine new relative positions:
Figure FDA0002311093860000033
wherein the content of the first and second substances,
Figure FDA0002311093860000034
Figure FDA0002311093860000035
4. the six-degree-of-freedom cooperative control method for preventing collision in spacecraft formation according to claim 1, wherein the step S2 comprises:
s2.1, definition
Figure FDA0002311093860000036
Determining a six-degree-of-freedom control model of the formation spacecraft as follows (10):
Figure FDA0002311093860000037
wherein the content of the first and second substances,
Figure FDA0002311093860000041
Figure FDA0002311093860000042
s2.2, determining a preset performance function as shown in a formula (11)
Figure FDA0002311093860000043
Where ρ isi0、ρi∞、liIs a preset normal number; rhoi0For presetting the initial value of the performance function, the selection is required to be more than x1Norm | | | x1An initial value of | l; rhoi∞For presetting the final value of the performance function, the state quantity x can be guaranteed1Finally converging to a stable region rhoi∞In the selection, the selection is required to be selected according to the precision requirement of the actual engineeringiThe error convergence rate can ensure that the system state is converged at least at an exponential rate, and the execution capacity of an actual system is considered during selection;
s2.3, determining a preset performance boundary:
definition of
Figure FDA0002311093860000044
Wherein x isdIs x1Desired terminal state of e1＝[e11…e16]T∈R6×1.e2＝[e21…e26]T∈R6×1Further considering the overshoot problem, the following preset performance boundaries are determined by using the preset performance function defined by equation (11):
Figure FDA0002311093860000045
β thereini∈[0，1]Is a design parameter;
s2.4, performing error model conversion, and introducing error transformation in the following form:
e1i(t)＝ρi(t)Ni(zi)，i＝1，…，6 (14)
wherein z isiIs the new conversion error; n is a radical ofi(zi) Is a smooth and reversible function with strict increment and satisfies
Figure FDA0002311093860000047
Converting equation (14) into equivalent
Figure FDA0002311093860000046
Determining Ni(zi)：
Figure FDA0002311093860000051
Can find out
Figure FDA0002311093860000052
Figure FDA0002311093860000053
Determining an equivalent system model of a six degree of freedom control model (10)
Figure FDA0002311093860000054
Wherein, z is defined as ═ z1，...，z6]T，
Figure FDA0002311093860000055
Figure FDA0002311093860000056
S2.5, according to the equivalent system model (19), determining a sliding mode surface as follows:
s＝x2+αz (20)
s2.6, determining a six-degree-of-freedom cooperative controller based on sliding mode variable structure control
u＝-g-1[f(x1，x2)+α(-rv+rΛ(x1)x2)+kss+Dsgn(s)](21)
Wherein, α, ksMore than 0 is sliding mode gain, and the gain D is diag (D)1，D2，D3，D4，D5，D6) And has Di＝sup(|di|)，i＝1，2，3。
5. The six-degree-of-freedom cooperative control method for preventing collision in spacecraft formation according to claim 4, wherein in order to reduce buffeting generated by symbolic terms sgn(s) in nature by sliding mode variable structure control, the symbolic terms sgn(s) are replaced by corresponding hyperbolic tangent functions in actual implementation of control.
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