CN114995518A - Master-slave cooperative guidance method for failure of slave aircraft GPS target positioning - Google Patents

Master-slave cooperative guidance method for failure of slave aircraft GPS target positioning Download PDF

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CN114995518A
CN114995518A CN202210888429.3A CN202210888429A CN114995518A CN 114995518 A CN114995518 A CN 114995518A CN 202210888429 A CN202210888429 A CN 202210888429A CN 114995518 A CN114995518 A CN 114995518A
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CN114995518B (en
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李国飞
李仕拓
吴云洁
吕金虎
凡永华
李博皓
刘晓东
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Northwestern Polytechnical University
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Abstract

The invention provides a master-slave cooperative guidance method when a slave aircraft GPS target positioning fails, which comprises the following steps: step 1: establishing a relative motion relation between the main aircraft and the target and between the auxiliary aircraft and the main aircraft; step 2: establishing an arrival time error variable of the main aircraft: and step 3: and (3) independently designing the guidance law of the main aircraft: and 4, step 4: defining a coordinated variable of the slave aircraft with respect to the master aircraft for consistency: and 5: and when the GPS positioning function is designed to be invalid, the slave aircraft collaboratively guides the law. By means of the method according to the invention, the master aircraft and the slave aircraft can be brought to the target position at the desired time. The method establishes a relative motion relation mathematical model of the aircraft, gives a guidance law of the main aircraft on the basis of constructing an arrival time error variable, further defines a consistent position cooperative variable, designs a cooperative guidance law of the slave aircraft, and realizes the consistency of the arrival time of all the slave aircraft and the main aircraft.

Description

Master-slave cooperative guidance method for failure of slave aircraft GPS target positioning
Technical Field
The invention relates to a master-slave type multi-aircraft cooperative guidance method, belonging to the field of aircraft guidance and control. The invention particularly relates to a cooperative guidance method which can still ensure that a master aircraft and a slave aircraft simultaneously reach a target point when the GPS target positioning function of the slave aircraft fails.
Background
Under the special application background of aircraft defense outburst, air cooperative operation, enclosure and the like, a plurality of aircrafts are sometimes required to arrive at a target point at the same time. Cooperative guidance becomes an important means for solving the problem of simultaneous arrival of multiple aircrafts due to the advantages of efficient fusion, cooperative complementation and information mutual assistance. According to the difference that the aircrafts undertake 'roles' in the group, the cooperative guidance method is divided into non-master cooperative guidance and master-slave cooperative guidance. Most of the existing cooperative guidance technologies require that all aircrafts can detect and locate target points, however, in a strong interference environment, the GPS locating function of the aircrafts is suppressed and interfered sometimes, so that the aircrafts cannot work normally, and at the moment, it is necessary to research the cooperative guidance technology when part of the aircrafts fail in the GPS locating function.
Disclosure of Invention
Aiming at the problem that a plurality of 'master-slave' aircrafts simultaneously reach a target point, the invention designs a 'master-slave' type cooperative guidance method which can still ensure that the target can be reached simultaneously when the GPS positioning function of the slave aircraft fails or the slave aircraft is not provided with a GPS positioning device in order to reduce the cost. The whole aircraft group consists of 1 main aircraft and a plurality of slave aircraft; according to the invention, the local motion relation of the master aircraft and the slave aircraft is constructed, and the cooperative guidance law is designed by means of networked information interaction, so that all the aircrafts can reach the target at the same time at the designated time.
The technical conception of the invention is as follows: on the basis of independently designing a guidance law of the master aircraft, a cooperative guidance law is designed for the slave aircraft, and the master aircraft and the slave aircraft are guaranteed to arrive at a target point at the same time at the designated time. Firstly, establishing a relative motion relation between a main aircraft and a target and between a slave aircraft and the main aircraft; secondly, giving a guidance law of the main aircraft to enable the main aircraft to reach a target at an expected time; and finally, constructing a consistency cooperative variable and giving a cooperative guidance law capable of synchronizing the arrival time of the slave aircraft and the arrival time of the master aircraft.
The invention discloses a master-slave cooperative guidance method when a slave aircraft GPS target positioning fails, which comprises the following steps: step 1: establishing a relative motion relation between the main aircraft and the target and between the auxiliary aircraft and the main aircraft;
each aircraft group comprises 1 main aircraft andnthe aircraft is driven by the aircraft. Algebraic graph theory may be employed to represent the communication relationships between aircraft. The communication relationship between the slave aircraft can be determined by using an adjacency matrixA=[a ij ]Is shown if it is the firsti（i=1, 2,…,n) One slave aircraft can be connected withj（j=1, 2,…,n, j≠i) The slave aircraft establishes a communication relationshipa ij =1, and otherwise,a ij = 0. The master aircraft can only transmit information to some slave aircraft satisfying the communication condition, but cannot receive information from the slave aircraft, and
Figure 100002_DEST_PATH_IMAGE001
is shown asiIf the communication relation between the slave aircraft and the master aircraft is received, the master aircraft receives the information of the master aircraft
Figure 100002_DEST_PATH_IMAGE002
Otherwise
Figure 100002_DEST_PATH_IMAGE003
. If any two aircraft nodes in the networked communication topology always have at least one communication path, the communication topology map is called a connected map. If the information transmission in the communication topological graph is bidirectional, the graph is called an undirected graph, and if a unidirectional information transmission link exists, the communication topological graph is called a directed graph.
The relationship of aircraft motion for a three-dimensional plane can be expressed as:
Figure 100002_DEST_PATH_IMAGE004
in the formula (2)x i , y i , z i ] T Denotes the firstiCoordinates of each aircraft in an inertial coordinate system; [v x,i , v y,i , v z,i ] T Is shown asiThe velocity vector of the aircraft in the inertial coordinate system,V i ，θ i andψ i respectively representing the speed, the track inclination angle and the track deflection angle of the aircraft, and satisfying the dynamic equation:
Figure 100002_DEST_PATH_IMAGE005
in the formula (I), the compound is shown in the specification,
Figure 100002_DEST_PATH_IMAGE006
、
Figure 100002_DEST_PATH_IMAGE007
and
Figure 100002_DEST_PATH_IMAGE008
respectively represent ballistic coordinate systemx, yAndzacceleration component of direction.
Defining an acceleration component in an inertial framea x,i, a y,i Anda z,i comprises the following steps:
Figure 100002_DEST_PATH_IMAGE009
acceleration component of inertial framea x,i, a y,i Anda z,i acceleration component of ballistic coordinate system
Figure 480984DEST_PATH_IMAGE006
、
Figure 100002_DEST_PATH_IMAGE010
And
Figure 100002_DEST_PATH_IMAGE011
the conversion relationship is as follows:
Figure 100002_DEST_PATH_IMAGE012
in the formula, a i And the acceleration vector is in an inertial coordinate system.
Under the coordinate system of the line of sightiThe relative motion relationship of the individual aircraft and the target may be expressed as:
Figure 100002_DEST_PATH_IMAGE013
in the formula (I), the compound is shown in the specification,R i is the distance of the aircraft relative to the target,ε i andη i indicating the inclination angle of the line of sight and the declination angle of the line of sight,
Figure 100002_DEST_PATH_IMAGE014
represents an acceleration vector in the line-of-sight coordinate system,La marker being a line of sight coordinate system;
the conversion relation of the acceleration vector from the inertial coordinate system to the sight line coordinate system is as follows:
Figure 100002_DEST_PATH_IMAGE015
the position information of the aircraft and the target is obtained by the following formulaR i ，ε i Andη i information:
Figure 100002_DEST_PATH_IMAGE016
in the formula (2)x t , y t , z t ] T Representing the coordinates of the target in an inertial coordinate system.
And 2, step: establishing an arrival time error variable of the main aircraft:
Figure 100002_DEST_PATH_IMAGE017
in the formula (I), the compound is shown in the specification,T d in order for the time of arrival instruction to be expected,t go to be the remaining time of flight,trepresenting the current time, is approximated by:
Figure 100002_DEST_PATH_IMAGE018
in the formula (I), the compound is shown in the specification,R 0 is the distance of the host aircraft from the target location point.
And step 3: and (3) independently designing the guidance law of the main aircraft:
Figure 100002_DEST_PATH_IMAGE019
in the formula (I), the compound is shown in the specification,R 0 is the distance of the host aircraft relative to the target,ε 0 andη 0 representing the inclination and declination of the line of sight of the host aircraft relative to the target,k 1,0 , k 2,0 andk 3,0 are positive real numbers.
Figure 100002_DEST_PATH_IMAGE020
，
Figure 100002_DEST_PATH_IMAGE021
，
Figure 100002_DEST_PATH_IMAGE022
Respectively are acceleration vectors under a sight line coordinate system;
and 4, step 4: defining a coordinated variable of the slave aircraft with respect to the master aircraft for consistency:
Figure 100002_DEST_PATH_IMAGE023
in the formula (I), the compound is shown in the specification,
Figure 100002_DEST_PATH_IMAGE024
a virtual control item is represented that is, x 0 , y 0 andz 0 representing the main aircraft in an inertial framex, yAndzthe coordinate position of the direction is determined,
Figure 100002_DEST_PATH_IMAGE025
and
Figure 100002_DEST_PATH_IMAGE026
is defined as:
Figure 100002_DEST_PATH_IMAGE027
in the formula (I), the compound is shown in the specification,p i,1 , p i,2 andp i,3 is a positive real proportionality coefficient.
And 5: when the GPS positioning function is designed to be invalid, the cooperative guidance law of the slave aircraft is as follows:
Figure 100002_DEST_PATH_IMAGE028
in the formula (I), the compound is shown in the specification,k i1, andk i2, is a positive real number, 0<μ 1 ,μ 2 , μ 3 <1,
Figure 100002_DEST_PATH_IMAGE029
An estimate of the disturbance term is not determined for the guidance system,ρ i andσ i are positive real numbers.
The invention has the beneficial effects that: the invention designs a master-slave type arrival time controllable cooperative guidance method with a slave aircraft GPS positioning function failure. In view of the fact that the slave aircraft cannot acquire the position information of the target, on the basis of independently giving a master aircraft guidance law, the slave aircraft defines a consistency cooperative variable by using the master aircraft state information, and designs a slave aircraft cooperative guidance law with controllable arrival time, so that the master aircraft and all the slave aircraft can arrive at the target position at the expected time.
Drawings
FIG. 1 is a schematic view of aircraft communication relationships.
Fig. 2 is a three-dimensional space flight trajectory curve.
FIG. 3 is a plot of aircraft to target distance.
FIG. 4 is a plot of the host aircraft time of arrival error, line of sight inclination, and line of sight declination response.
FIG. 5 is a consistent covariateξ ,i1 And (6) responding.
FIG. 6 is a consistent covariateξ ,i2 And (6) responding.
FIG. 7 is a plot of normal acceleration from the aircraft.
Detailed Description
The present invention will be further described with reference to fig. 1-7.
The invention discloses a master-slave cooperative guidance method when a slave aircraft GPS target positioning fails, which comprises the following steps:
step 1: establishing a relative motion relation between the main aircraft and the target and between the auxiliary aircraft and the main aircraft;
suppose that a cluster of aircraft each contains 1 host aircraft andnthe aircraft is driven by the aircraft. Algebraic graph theory may be employed to represent the communication relationships between aircraft. The communication relationship between the slave aircraft can be determined by using an adjacency matrixA=[a ij ]To show if it is the firsti（i=1, 2,…,n) One slave aircraft can be connected withj（j=1, 2,…,n, j≠i) The slave aircraft establishes a communication relationshipa ij =1, and otherwise,a ij and = 0. The master aircraft can only transmit information to some slave aircraft satisfying the communication condition, but cannot receive information from the slave aircraft, and
Figure 880348DEST_PATH_IMAGE001
is shown asiIf the communication relation between the slave aircraft and the master aircraft is received, the master aircraft receives the information of the master aircraft
Figure 128927DEST_PATH_IMAGE002
Otherwise
Figure 258557DEST_PATH_IMAGE003
. If any two aircraft nodes in the networked communication topology always have at least one communication path, the communication topology map is called a connected map. If the information transmission in the communication topological graph is bidirectional, the graph is called an undirected graph, and if a unidirectional information transmission link exists, the communication topological graph is called a directed graph.
The relationship of aircraft motion for a three-dimensional plane can be expressed as:
Figure 541770DEST_PATH_IMAGE004
in the formula (2)x i , y i , z i ] T Denotes the firstiCoordinates of the individual aircraft in an inertial coordinate system; [v x,i , v y,i , v z,i ] T Is shown asiThe velocity vector of the aircraft in the inertial coordinate system,V i ，θ i andψ i respectively representing the speed, the track inclination angle and the track deflection angle of the aircraft, and satisfying the dynamic equation:
Figure 82342DEST_PATH_IMAGE005
in the formula (I), the compound is shown in the specification,
Figure 21479DEST_PATH_IMAGE006
、
Figure 689221DEST_PATH_IMAGE007
and
Figure 341788DEST_PATH_IMAGE008
respectively represent ballistic coordinate systemx, yAndzacceleration component of direction.
Defining an acceleration component in an inertial framea x,i, a y,i Anda z,i comprises the following steps:
Figure 803993DEST_PATH_IMAGE009
acceleration component of inertial framea x,i, a y,i Anda z,i acceleration component of ballistic coordinate system
Figure 230427DEST_PATH_IMAGE006
、
Figure 685548DEST_PATH_IMAGE010
And
Figure 943354DEST_PATH_IMAGE011
the conversion relationship is as follows:
Figure 842039DEST_PATH_IMAGE012
in the formula, a i The acceleration vector under the inertial coordinate system is obtained.
Under the coordinate system of the line of sightiThe relative motion relationship of the individual aircraft and the target may be expressed as:
Figure 5036DEST_PATH_IMAGE013
in the formula (I), the compound is shown in the specification,R i is the distance of the aircraft relative to the target,ε i andη i indicating the inclination angle of the line of sight and the declination angle of the line of sight,
Figure 749002DEST_PATH_IMAGE014
represents an acceleration vector in the line-of-sight coordinate system,La marker being a line of sight coordinate system;
the conversion relation of the acceleration vector from the inertial coordinate system to the sight line coordinate system is as follows:
Figure 126893DEST_PATH_IMAGE015
the position information of the aircraft and the target is obtained by the following formulaR i ，ε i Andη i information:
Figure 930901DEST_PATH_IMAGE016
in the formula (2)x t , y t , z t ] T Representing the position coordinates of the target in an inertial coordinate system.
Step 2: establishing an arrival time error variable of the main aircraft:
Figure 315615DEST_PATH_IMAGE017
in the formula (I), the compound is shown in the specification,T d in order for the time of arrival instruction to be expected,t go to be the remaining time of flight for the time,trepresenting the current time, is approximated by:
Figure 315801DEST_PATH_IMAGE018
in the formula (I), the compound is shown in the specification,R 0 is a main aircraft anddistance of the target location point.
And step 3: and (3) independently designing the guidance law of the main aircraft:
Figure 282620DEST_PATH_IMAGE019
in the formula (I), the compound is shown in the specification,R 0 is the distance of the host aircraft relative to the target,ε 0 andη 0 representing the inclination and declination of the line of sight of the host aircraft relative to the target,k 1,0 , k 2,0 andk 3,0 are positive real numbers.
Figure 788688DEST_PATH_IMAGE020
，
Figure 208168DEST_PATH_IMAGE021
，
Figure 12044DEST_PATH_IMAGE022
Respectively are acceleration vectors under a sight line coordinate system;
and 4, step 4: defining a coordinated variable of the slave aircraft with respect to the master aircraft for consistency:
Figure 833370DEST_PATH_IMAGE023
in the formula (I), the compound is shown in the specification,
Figure 510339DEST_PATH_IMAGE024
a virtual control item is represented that is, x 0 , y 0 andz 0 representing the main aircraft in an inertial framex, yAndzthe coordinate position of the direction is determined,
Figure 666383DEST_PATH_IMAGE025
and
Figure 759104DEST_PATH_IMAGE026
is defined as:
Figure 700515DEST_PATH_IMAGE027
in the formula (I), the compound is shown in the specification,p i,1 , p i,2 andp i,3 is a positive real proportionality coefficient.
And 5: when the GPS positioning function is designed to be invalid, the cooperative guidance law of the slave aircraft is as follows:
Figure 797653DEST_PATH_IMAGE028
in the formula (I), the compound is shown in the specification,k i1, andk i2, is a positive real number, 0<μ 1 ,μ 2 , μ 3 <1,
Figure 191725DEST_PATH_IMAGE029
An estimate of the disturbance term is not determined for the guidance system,ρ i andσ i are positive real numbers.
And verifying the master-slave type cooperative guidance method with controllable arrival time when the designed slave aircraft GPS positioning function fails by utilizing a Matlab/Simulink simulation platform. For the embodiment, 1 master aircraft and 3 slave aircraft are selected, and the inter-missile communication topological relation is shown in fig. 1, wherein 0 represents the master aircraft, and 1, 2 and 3 represent the 1 st, 2 and 3 rd slave aircraft respectively. Target position (0m, 0m, 0m), speed of the host aircraftV 0 At 330m/s, the initial speed of the aircraft isV 1 =350m/s，V 2 =310m/s，V 3 =310 m/s. The initial position of the main aircraft is (4048m, 8500m, 7565m), and the initial positions of the auxiliary aircraft are as follows: (5960m, 6191m, 9596m), (6561m, 5000m, 4680m) and (8116m, 7382m, 5910 m). The aircraft overload limit is 20 g. The parameters are set as follows:T d =35s, k 1,0 =k 2,0 =k 3,0 =10, k i1, =5, k i2, =8 for i=1,2,3, μ 1 =μ 2 =μ 3 =0.5, ρ i =0.05, σ i =0.03, p 1 , 1 =p 1 , 2 =p 1 , 3 =0.2,
p 2 , 1 =p 2 , 2 =p 2 , 3 =0.4, p 3 , 1 =p 3 , 2 = p 3 , 3 =0.6。
the simulation results are shown in fig. 2-7, and according to the three-dimensional space motion trail and the aircraft-to-target distance curve, under the master-slave type arrival time controllable cooperative guidance mode with the failed slave aircraft GPS positioning function, all the aircraft can arrive at the target position at the expected time 35s, and the arrival time of each slave aircraft is consistent with the arrival time of the master aircraft. The arrival time error variable, the sight line inclination angle, the sight line deflection angle, the consistency cooperative variable of the slave aircraft and the like of the master aircraft can be stably converged, and the acceleration output gradually tends to be stable after being subjected to transient state adjustment.

Claims (4)

1. A master-slave cooperative guidance method when a slave aircraft GPS target positioning fails is characterized by comprising the following steps:
step 1: establishing a relative motion relation between the main aircraft and the target and between the auxiliary aircraft and the main aircraft;
the motion relation of the aircraft under the three-dimensional plane is expressed as follows:
Figure DEST_PATH_IMAGE001
in the formula (2)x i , y i , z i ] T Is shown asiCoordinates of the individual aircraft in an inertial coordinate system; [v x,i , v y,i , v z,i ] T Is shown asiThe velocity vector of the aircraft in the inertial coordinate system,V i ，θ i andψ i respectively representing the speed, the track inclination angle and the track deflection angle of the aircraft, and satisfying the dynamic equation:
Figure DEST_PATH_IMAGE002
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE003
、
Figure DEST_PATH_IMAGE004
and
Figure DEST_PATH_IMAGE005
respectively represent ballistic coordinate systemx, yAndzan acceleration component of direction;
defining an acceleration component in an inertial framea x,i, a y,i Anda z,i comprises the following steps:
Figure DEST_PATH_IMAGE006
acceleration component of inertial framea x,i, a y,i Anda z,i acceleration component of ballistic coordinate system
Figure 964144DEST_PATH_IMAGE003
、
Figure DEST_PATH_IMAGE007
And
Figure DEST_PATH_IMAGE008
the conversion relationship is as follows:
Figure DEST_PATH_IMAGE009
in the formula, a i An acceleration vector under an inertial coordinate system;
under the coordinate system of the line of sightiThe relative motion relationship of the individual aircraft and the target is expressed as:
Figure DEST_PATH_IMAGE010
in the formula (I), the compound is shown in the specification,R i is the distance of the aircraft relative to the target,ε i andη i indicating the inclination angle of the line of sight and the declination angle of the line of sight,
Figure DEST_PATH_IMAGE011
represents an acceleration vector in the line-of-sight coordinate system,La marker being a line of sight coordinate system;
the conversion relation of the acceleration vector from the inertial coordinate system to the sight line coordinate system is as follows:
Figure DEST_PATH_IMAGE012
and 2, step: establishing an arrival time error variable of the main aircraft:
Figure DEST_PATH_IMAGE013
in the formula (I), the compound is shown in the specification,T d in order for the time of arrival instruction to be expected,t go to be the remaining time of flight,trepresenting the current time, is approximated by:
Figure DEST_PATH_IMAGE014
in the formula (I), the compound is shown in the specification,R 0 of the main aircraft with a target locationA distance;
and step 3: and (3) independently designing the guidance law of the main aircraft:
Figure DEST_PATH_IMAGE015
in the formula (I), the compound is shown in the specification,R 0 is the distance of the host aircraft relative to the target,ε 0 andη 0 representing the inclination and declination of the line of sight of the host aircraft relative to the target,k 1,0 , k 2,0 andk 3,0 is a positive real number;
Figure DEST_PATH_IMAGE016
，
Figure DEST_PATH_IMAGE017
，
Figure DEST_PATH_IMAGE018
acceleration vectors under a sight line coordinate system are respectively;
and 4, step 4: defining a coordinated variable of the slave aircraft with respect to the master aircraft for consistency:
Figure DEST_PATH_IMAGE019
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE020
a virtual control item is represented that is, x 0 , y 0 andz 0 representing the host aircraft in an inertial framex, yAndzthe coordinate position of the direction is determined,
Figure DEST_PATH_IMAGE021
and
Figure DEST_PATH_IMAGE022
is defined as:
Figure DEST_PATH_IMAGE023
in the formula (I), the compound is shown in the specification,p i,1 , p i,2 andp i,3 is a positive real number proportionality coefficient;
and 5: when the GPS positioning function is designed to be invalid, the cooperative guidance law of the slave aircraft is as follows:
Figure DEST_PATH_IMAGE024
in the formula (I), the compound is shown in the specification,k i1, andk i2, is a positive real number, 0<μ 1 ,μ 2 , μ 3 <1,
Figure DEST_PATH_IMAGE025
An estimate of the disturbance term is not determined for the guidance system,ρ i andσ i are positive real numbers.
2. The master-slave cooperative guidance method in the event of a slave aircraft GPS target location failure according to claim 1, characterized in that: each aircraft group comprises 1 main aircraft andna slave aircraft; representing the communication relation between the aircrafts by adopting algebraic graph theory; adjacency matrix for communication relationships between slave aircraftA=[a ij ]To indicate ifiOne slave aircraft can be connected withjA slave aircraft establishes a communication relationship, thena ij =1, and otherwise,a ij =0；i=1, 2,…,n；j=1, 2,…,n, j≠i。
3. the master-slave cooperative guidance method in the event of a slave aircraft GPS target location failure according to claim 2, characterized in that: the main aircraft can only send information toPart of the slave aircraft satisfying the communication conditions, but not receiving information from the aircraft, using
Figure DEST_PATH_IMAGE026
Denotes the firstiThe communication relation between the slave aircraft and the master aircraft is determined if the information of the master aircraft is received
Figure DEST_PATH_IMAGE027
Otherwise
Figure DEST_PATH_IMAGE028
。
4. The master-slave cooperative guidance method in the event of a slave aircraft GPS target location failure according to claim 1, characterized in that: obtained by calculation of the formulaR i ，ε i Andη i information:
Figure DEST_PATH_IMAGE029
in the formula (2)x t , y t , z t ] T Representing the coordinates of the target in an inertial coordinate system.
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