CN110550240B - Method for intercepting multi-star cooperative game - Google Patents
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Abstract
The invention discloses a multi-star cooperative game interception method, and relates to a multi-star cooperative interception method. The invention aims to solve the problems that the existing single satellite has too long interception time and the maneuverability of a target satellite is not considered. Acquiring situation information of an interception star and a target star through a sensor, and calculating zero control miss distance of the interception star and the target star and zero control miss distance between the interception stars based on the situation information; secondly, designing a game index function to enable the intercepting stars to intercept the target star without mutual collision; thirdly, solving a game strategy of the intercepted star and the target star; solving the optimal interception end time under different interception situations, and calculating the optimal zero control miss amount to obtain an optimal interception star and target star game strategy; and fifthly, controlling the flight track of each interception satellite according to the optimal interception satellite game strategy, and approaching the target satellite to realize interception. The method is used for the field of multi-satellite cooperative interception.
Description
Technical Field
The invention relates to a multi-satellite cooperation intercepting method.
Background
The satellite is an important component of a spatial information network, and has the advantages of long communication distance, no limitation of terrain and the like in the aspect of information communication. In order to capture the space information dominance, satellite interception is a necessary means for future space balance. With the development of satellite intellectualization, the target satellite can sense the spatial situation, acquire corresponding spatial information and make a decision to deal with the battlefield situation, which puts higher requirements on the interception of the satellite.
Because the target satellite has spatial perception capability, autonomous decision-making capability and maneuvering capability, situation information can be obtained in the process of intercepting satellite approaching, and an optimal strategy is adopted to avoid, while in the traditional satellite intercepting method, the maneuverability or the maneuvering optimality of the target satellite is not considered, so that the intercepting satellite cannot intercept the target according to a preset track, and meanwhile, the defects of overlong intercepting time and the like exist for single-satellite intercepting.
"limited time control of relative orbit of spacecraft near non-cooperative target" published in university of college graduates in 11 months 2013, author: wu Cheng nan, etc. The article does not consider the optimality of target star maneuvering, although it considers the maneuvering capabilities of the target star.
"satellite terminal pursuit control method based on zero control miss distance", published in "university of physical engineers college of beijing" at 11 months in 2016, the author: wangqiang and the like. The control method under single-star game interception is provided, but the required interception time is long, and the quick interception is difficult to realize.
Therefore, for multi-satellite cooperative game interception, the game strategy of each intercepted satellite is designed through the game index function, the target satellite can be intercepted quickly, and the effectiveness of the interception strategy is obviously improved.
Disclosure of Invention
The invention aims to provide a multi-satellite cooperative game interception method for solving the problems that the existing single-satellite interception time is too long and the maneuverability of a target satellite is not considered.
The specific process of the interception method of the multi-star cooperative game is as follows:
acquiring situation information of an interception star and a target star through a sensor, and calculating zero control miss distance of the interception star and the target star and zero control miss distance between the interception stars based on the situation information;
the situation information comprises the position and speed information of an interception star and a target star under the track coordinate system;
secondly, designing a game index function to enable the intercepting stars to intercept the target star without mutual collision;
step three, solving the game strategy of the interception star and the target star;
solving the optimal interception end time under different interception situations, calculating the optimal zero control miss amount based on the optimal interception end time and the zero control miss amount of the interception star and the target star, and optimizing the game strategy of the interception star and the target star according to the optimal zero control miss amount to obtain the optimal interception star and target star game strategy;
and step five, controlling the flight track of each interception star according to the optimal interception star game strategy, and approaching the target star to realize interception.
The invention has the beneficial effects that:
the invention discloses a multi-satellite cooperative game interception method, which comprises the steps of establishing an orbit coordinate system with a reference satellite as an origin on the basis that a given reference satellite orbit is a circular orbit, and establishing a relative state variable and a state transfer matrix of an intercepted satellite and a target satellite under the orbit coordinate system. And then zero control miss distance is introduced, and the game strategy of each intercepted star and the target star is designed by taking the terminal miss distance as an index function. And finally, substituting the game strategies of the intercepted stars and the target stars into a reduced order kinetic equation and integrating the game strategies, combining the game strategies with another function of zero control miss distance related to the remaining time, and solving the optimal interception ending time to obtain the optimal game strategy, so that the problems that the existing single star has overlong interception time and the maneuverability of the target star is not considered are solved.
According to the multi-satellite cooperation game interception method disclosed by the invention, the target satellites are intercepted by adopting a plurality of interception satellites simultaneously, the rapid interception is realized on the basis of considering the strategic optimality of the target satellites, and compared with single-satellite interception, the interception time can be shortened by 39.21 s.
According to the multi-satellite cooperative game interception method disclosed by the invention, the interception end time can be obtained in a self-adaptive manner by solving the equation set related to the remaining time, and the uncertainty of the interception end time selection is reduced, so that the adaptability is good.
Drawings
FIG. 1 is a schematic view of an orbital coordinate system of the present invention;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a diagram of simulation results of multi-satellite cooperative game interception performed according to the method of the present invention, where x, y, and z are coordinate axes of an orbit coordinate system;
fig. 4 is a simulation result diagram of single star game interception.
Detailed Description
The first embodiment is as follows: the specific process of the interception method of the multi-star cooperative game in the embodiment is as follows:
the invention provides a multi-satellite cooperative game interception method, wherein an interception satellite and a target satellite are regarded as game parties, and strategies for intercepting the satellite are designed under the condition of fully considering the strategy of the target satellite, so that the target satellite is quickly intercepted. The concrete implementation is as follows:
acquiring situation information of an interception star and a target star through a sensor, and calculating zero control miss distance of the interception star and the target star and zero control miss distance between the interception stars based on the situation information;
the situation information comprises the position and speed information of an interception star and a target star under the track coordinate system;
secondly, designing a game index function to enable the intercepting stars to quickly intercept the target stars without mutual collision;
solving a game strategy of the intercepted star and the target star based on a differential strategy theory;
step four, adaptively solving the optimal interception ending time under different interception situations, calculating the optimal zero control miss distance based on the optimal interception ending time and the zero control miss distance of the intercepted star and the target star, optimizing the game strategies (5) and (6) of the intercepted star and the target star according to the optimal zero control miss distance, and obtaining the optimal game strategy of the intercepted star and the target star (t is the optimal interception ending time which is firstly substituted into the formula 1fSubstituting equation 1 into equations 5 and 6);
and fifthly, controlling the flight track of each interception star according to the optimal interception star game strategy, and quickly approaching a target star to realize interception.
The solving flow chart of the multi-star game interception is shown in figure 2.
The second embodiment is as follows: the first step is that situation information of the interception stars and the target stars is obtained through the sensor, and zero control miss distance between the interception stars and the target stars and zero control miss distance between the interception stars are calculated based on the situation information;
the situation information comprises the position and speed information of an interception star and a target star under the track coordinate system;
the specific process is as follows:
establishing a reference satellite running on a circular orbit at the initial position of the interception satellite, wherein the orbit of the reference satellite is a curve in the graph of figure 1, and the position vector diameter of the interception satellite P and the geocenter is r2The vector of the position of the reference satellite and the geocenter is r1The vector diameter of the relative position of the interception satellite and the reference satellite is delta r ═ r2-r1(ii) a Taking a reference satellite as an origin, establishing an orbit coordinate system as shown in figure 1, wherein the origin O of the orbit coordinate system1In the reference satellite, orbital coordinate system O1The x-axis pointing from the earth's center to the reference satellite, orbital coordinate system O1The z-axis being perpendicular to the orbital plane of the reference satellite, the orbital coordinate system O1y axis and O1x-axis, O1The z axis forms a right-hand rectangular coordinate system;
adopting N interception stars to cooperatively intercept 1 target star, defining the position and speed of each star in the orbit coordinate system as state variables of each star, and calculating the relative state of each interception star and the target star as
Wherein,
for the relative state of the i-th intercepting star and the target star,
state variable, X, for the ith interceptor starEThe state variable of the target star, and N is the number of the interception stars;
calculating zero control miss distance of the interception star and the target star:
calculating zero control miss distance between the interception satellites:
wherein,
zero control miss distance between the ith intercepted star and the target star, t is the current time of interception, t isfIn order to be the end time of the interception,
the relative state of the I-th intercepting star and the target star, D is a given matrix, and D is ═ I3 03]，I3Is a 3 × 3 unit array, 03Is a zero matrix of 3 x 3,
the zero control miss distance of the ith interception star and the jth interception star,
zero control miss distance between the jth interception star and the target star, i represents the ith interception star, j represents the jth interception star, and i is not equal to j, phi (t)fAnd t) is the state transition matrix of the satellite.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: in this embodiment, the state transition matrix of the satellite is different from the state transition matrix of the satellite
Φ11、Φ12、Φ21、Φ22Is an intermediate variable;
where ω is an orbital angular velocity of the reference satellite, τ is a difference between the interception end time and the current time, and τ is tfT, t is the intercept current time, tfIs the interception end time.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the second step is to design a game index function, so that the intercepting stars can quickly intercept the target stars without mutual collision; the specific process is as follows:
defining the game index function of the interceptor star and the target star as
Wherein J is a game index function of the intercepting star and the target star,
for the game strategy of the 1 st blocker star,
game strategy for the Nth blocker star, UEIs the game strategy of the target star,
for intercepting items, the intercepting star is controlled to quickly reduce the distance between the intercepting star and the target star,
the zero control miss distance k of the ith intercepted star and the target star at the end of interceptioniIs a comprehensive weight and satisfies k being more than or equal to 0i≤1，
For collision avoidance items, the interception stars are controlled not to collide with each other,
the zero control miss distance r of the ith interception star and the jth interception star at the end of interceptionijIs a penalty factor.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the present embodiment is different from the first to the fourth embodiments in that the penalty factor rijComprises the following steps:
wherein m is the safety distance between the interception stars.
Other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: the difference between the embodiment and one of the first to fifth embodiments is that, in the third step, the game strategy of the intercepted star and the target star is solved based on a differential game theory; the specific process is as follows:
according to the game index function, the game strategy of each interceptor star is designed to be
The game strategy of the target star is
Wherein,
is the intermediate variable(s) of the variable,
for the maximum thrust amplitude of the ith intercept star,
the game strategy of the ith intercepted star is T, and T is transposition;
is an intermediate variable, pEMaximum thrust amplitude, U, of the target satelliteEIs a game strategy of the target star.
Other steps and parameters are the same as those in one of the first to fifth embodiments.
The seventh embodiment: this embodiment differs from one of the first to sixth embodiments in that the intermediate variable is
Φ(tfT) is the state transition matrix of the satellite, D, B is a given matrix, D ═ I3 03]，B＝[03 I3]T，I3Is a 3 × 3 unit array, 03A zero matrix of 3 × 3;
the intermediate variable
Other steps and parameters are the same as those in one of the first to sixth embodiments.
The specific implementation mode is eight: the implementation mode is different from one of the first to sixth implementation modes in that the fourth step is used for adaptively solving the optimal interception end time under different interception situations, calculating the optimal zero control miss amount based on the optimal interception end time and the zero control miss amount of the intercepted star and the target star, and optimizing the game strategies (5) and (6) of the intercepted star and the target star according to the optimal zero control miss amount to obtain the optimal game strategies of the intercepted star and the target star; the specific process is as follows:
substituting the game strategy (5) of each interceptor satellite and the game strategy (6) of the target satellite into the reduced order kinetic equation of the interceptor satellite and the target satellite, and using the residual time tgoObtaining zero control miss distance for integral variable integralAt the remaining time tgoFunctional relationship of (a):
tgo＝tf-t；fi(tgo) As an intermediate variable, the zero control miss distance of the ith interception star and the target star obtained by integration relates to the residual time tgoThe functional relationship of (a);
the order-reduced kinetic equation of the interception star and the target star is as follows
Wherein,
is composed of
The first derivative of (a);
for a given interception initial condition
Comprises the relative position and relative speed of the ith interception star and the target star under the orbit coordinate system at the initial interception moment, and changes the interception ending time tfObtaining zero control miss amount with respect to residual time tgoAnother functional relationship of
Wherein,
zero miss control amount for the ith interception star and the target star with respect to the remaining time tgoA relationship of (c), phi (t)go) State transition matrix for satellite with respect to time remaining tgoIn the context of (a) or (b),
to intercept the relative state of the 1 st intercepted star and the target star at the initial moment, t0Is the initial time of interception;
for N interceptors, two zero-control miss-target expression expressions (7) and (8) are respectively combined to obtain an equation set related to the residual time, the equation set related to the residual time is solved, and the minimum solution is recorded as
Therefore, the optimal interception end time is
Other steps and parameters are the same as those in one of the first to seventh embodiments.
The specific implementation method nine: in this embodiment, the remaining time equation set is as follows, unlike the first to eighth embodiments
Wherein f is1(tgo) Zero control miss amount of the 1 st interception star and the target star obtained for integration with respect to the remaining time tgoThe functional relationship of (a) to (b),
to intercept the relative state of the 1 st intercepted star and the target star at the initial moment, t0To intercept the initial time, fN(tgo) Obtaining zero control miss amount of the Nth interception star and the target star for the residual time tgoThe functional relationship of (a) to (b),
the relative state of the Nth interception star and the target star at the initial interception moment.
Other steps and parameters are the same as those in one to eight of the embodiments.
The detailed implementation mode is ten: this embodimentThe difference between the above formula and one of the first to ninth embodiments is that the orbital angular velocity of the reference satellite for circular orbit
Mu is earth constant, mu is 3.986 × 105km3/s2And a is the orbit semi-major axis of the reference satellite.
Other steps and parameters are the same as those in one of the first to ninth embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows: the orbital altitude of the reference satellite is selected to be 36000km, the earth radius is assumed to be 6378km, and the orbital angular velocity is calculated to be omega-7.2 × 10-5rad/s. In order to verify the advantages of the method in satellite interception, simulation analysis is respectively carried out on multi-satellite cooperative game interception and single-satellite game interception.
Firstly, the simulation of multi-satellite cooperative game interception is given, and two intercepted satellites P exist in the space1，P2And a target star E, wherein the intercept star P1The initial position of [ 3; 1; 0]km, initial speed [ 0.01; 0; 0]km/s, maximum thrust amplitude
Intercept star P2Is [ 0; 0; 0]km, initial speed [ -0.005; 0; 0.005]km/s, maximum thrust amplitude
The initial position of the interceptor star E is [ 2; 0; 1]km, initial speed [ 0; 0.005; 0]km/s, maximum thrust amplitude
The integrated weight k1＝k2When the time is 0.5, the optimal interception ending time is 79.79s and the interception star P is obtained through the equation set (9)1，P2And the motion trajectory of the target star E is as shown in fig. 3.
The simulation of single-star game interception is given below, and one interception exists in the spaceStar P1And a target star E, wherein the intercept star P1The initial position of [ 3; 1; 0]km, initial speed [ 0.01; 0; 0]km/s, maximum thrust amplitude
The initial position of the interceptor star E is [ 2; 0; 1]km, initial speed [ 0; 0.005; 0]km/s, maximum thrust amplitude
Obtaining the optimal interception end time of 119s and the interception star P through an equation set (9)1And the motion trajectory of the target star E is as shown in fig. 4.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.
Claims (7)
1. The method for intercepting the multi-star cooperative game is characterized by comprising the following steps: the method comprises the following specific processes:
acquiring situation information of an interception star and a target star through a sensor, and calculating zero control miss distance of the interception star and the target star and zero control miss distance between the interception stars based on the situation information;
the situation information comprises the position and speed information of an interception star and a target star under the track coordinate system;
secondly, designing a game index function to enable the intercepting stars to intercept the target star without mutual collision;
step three, solving the game strategy of the interception star and the target star;
solving the optimal interception end time under different interception situations, calculating the optimal zero control miss amount based on the optimal interception end time and the zero control miss amount of the interception star and the target star, and optimizing the game strategy of the interception star and the target star according to the optimal zero control miss amount to obtain the optimal interception star and target star game strategy;
fifthly, controlling the flight track of each interception satellite according to an optimal interception satellite game strategy, and approaching a target satellite to realize interception;
acquiring situation information of the interception stars and the target star through a sensor, and calculating zero control miss distance of the interception stars and the target star and zero control miss distance between the interception stars based on the situation information;
the situation information comprises the position and speed information of an interception star and a target star under the track coordinate system;
the specific process is as follows:
the position vector diameter of the interception star P and the geocenter is r2The vector of the position of the reference satellite and the geocenter is r1The vector diameter of the relative position of the interception satellite and the reference satellite is delta r ═ r2-r1(ii) a Establishing an orbit coordinate system by taking a reference satellite as an origin, wherein the origin O of the orbit coordinate system1In the reference satellite, orbital coordinate system O1The x-axis pointing from the earth's center to the reference satellite, orbital coordinate system O1The z-axis being perpendicular to the orbital plane of the reference satellite, the orbital coordinate system O1y axis and O1x-axis, O1The z axis forms a right-hand rectangular coordinate system;
adopting N interception stars to cooperatively intercept 1 target star, defining the position and speed of each star in the orbit coordinate system as state variables of each star, and calculating the relative state of each interception star and the target star as
Wherein,
for the relative state of the i-th intercepting star and the target star,
state variable, X, for the ith interceptor starEThe state variable of the target star, and N is the number of the interception stars;
calculating zero control miss distance of the interception star and the target star:
calculating zero control miss distance between the interception satellites:
wherein,
zero control miss distance between the ith intercepted star and the target star, t is the current time of interception, t isfIn order to be the end time of the interception,
the relative state of the I-th intercepting star and the target star, D is a given matrix, and D is ═ I3 03]，I3Is a 3 × 3 unit array, 03Is a zero matrix of 3 x 3,
the zero control miss distance of the ith interception star and the jth interception star,
zero control miss distance between the jth interception star and the target star, i represents the ith interception star, j represents the jth interception star, and i is not equal to j, phi (t)fAnd t) is a state transition matrix of the satellite;
state transition matrix of the satellite
Φ11、Φ12、Φ21、Φ22Is an intermediate variable;
where ω is an orbital angular velocity of the reference satellite, τ is a difference between the interception end time and the current time, and τ is tfT, t is the intercept current time, tfIs the interception end time;
designing a game index function in the second step to enable the interception stars to intercept the target star without mutual collision; the specific process is as follows:
defining the game index function of the interceptor star and the target star as
Wherein J is a game index function of the intercepting star and the target star,
for the game strategy of the 1 st blocker star,
game strategy for the Nth blocker star, UEIs the game strategy of the target star,
for the interception item, the distance between the interception star and the target star is controlled,
the zero control miss distance k of the ith intercepted star and the target star at the end of interceptioniIs a comprehensive weight and satisfies k being more than or equal to 0i≤1，
For collision avoidance items, the interception stars are controlled not to collide with each other,
the zero control miss distance r of the ith interception star and the jth interception star at the end of interceptionijIs a penalty factor.
2. The method for intercepting a multi-star cooperative game as claimed in claim 1, wherein: the penalty factor rijComprises the following steps:
wherein m is the safety distance between the interception stars.
3. The method for intercepting a multi-star cooperative game as claimed in claim 2, wherein: solving the game strategy of the intercepted star and the target star in the third step; the specific process is as follows:
according to the game index function, the game strategy of each interceptor star is designed to be
The game strategy of the target star is
Wherein,
is an intermediate variable, ρ PiFor the maximum thrust amplitude of the ith intercept star,
the game strategy of the ith intercepted star is T, and T is transposition;
is an intermediate variable, pEMaximum thrust amplitude, U, of the target satelliteEIs a game strategy of the target star.
4. The method for intercepting a multi-star cooperative game as recited in claim 3, wherein: the intermediate variable
Φ(tfT) is the state transition matrix of the satellite, D, B is a given matrix, D ═ I3 03]，B＝[03 I3]T，I3Is a 3 × 3 unit array, 03A zero matrix of 3 × 3;
the intermediate variable
5. The method for intercepting a multi-star cooperative game as recited in claim 4, wherein: solving the optimal interception ending time under different interception situations, calculating the optimal zero control miss amount based on the optimal interception ending time and the zero control miss amount of the intercepted star and the target star, and optimizing the game strategy of the intercepted star and the target star according to the optimal zero control miss amount to obtain the optimal game strategy of the intercepted star and the target star; the specific process is as follows:
substituting the game strategy (5) of each interceptor satellite and the game strategy (6) of the target satellite into the reduced order kinetic equation of the interceptor satellite and the target satellite, and using the residual time tgoObtaining zero control miss amount for integral variable integral with respect to residual time tgoFunctional relationship of (a):
tgo＝tf-t；fi(tgo) Is an intermediate variable;
the order-reduced kinetic equation of the interception star and the target star is as follows
Wherein,
is composed of
The first derivative of (a);
for a given interception initial condition
Comprises the relative position and relative speed of the ith interception star and the target star under the orbit coordinate system at the initial interception moment, and changes the interception ending time tfObtaining zero control miss amount with respect to residual time tgoAnother functional relationship of
Wherein,
zero miss control amount for the ith interception star and the target star with respect to the remaining time tgoA relationship of (c), phi (t)go) State transition matrix for satellite with respect to time remaining tgoIn the context of (a) or (b),
to intercept the relative state of the 1 st intercepted star and the target star at the initial moment, t0Is the initial time of interception;
for N interceptors, two zero-control miss-target expression expressions (7) and (8) are respectively combined to obtain an equation set related to the residual time, the equation set related to the residual time is solved, and the minimum solution is recorded as
Therefore, the optimal interception end time is
6. The method for intercepting a multi-star cooperative game as recited in claim 5, wherein: the equation set regarding the remaining time is as follows
Wherein f is1(tgo) Zero control miss amount of the 1 st interception star and the target star obtained for integration with respect to the remaining time tgoThe functional relationship of (a) to (b),
to intercept the relative state of the 1 st intercepted star and the target star at the initial moment, t0To intercept the initial time, fN(tgo) Obtaining zero control miss amount of the Nth interception star and the target star for the residual time tgoThe functional relationship of (a) to (b),
the relative state of the Nth interception star and the target star at the initial interception moment.
7. The method for intercepting a multi-star cooperative game as recited in claim 6, wherein the method further comprisesThe method comprises the following steps: orbital angular velocity of the reference satellite
Mu is earth constant, mu is 3.986 × 105km3/s2And a is the orbit semi-major axis of the reference satellite.
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