CN117519228A - Aircraft maneuvering formation control method based on distributed extended state observer - Google Patents
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Abstract
The invention designs an aircraft formation control method based on a distributed extended state observer, which enables an aircraft group with a 'collar-slave' type structure to fly according to an expected formation. The method comprises the steps of enabling all followers to estimate the position and speed information of a leader through a distributed extended state observer. Then a coordinate transformation matrix is calculated according to the speed estimation value, and the expected position of the follower in the inertia space is calculated according to the coordinate transformation matrix and the position estimation value. And finally, controlling the follower to track the expected position through a position tracking control law, thereby realizing the expected formation. In this method, the information interaction between the followers only involves an estimate of the leader position, and the formation direction is kept consistent with the leader flight direction.
Description
Technical Field
The invention designs an aircraft maneuvering formation control method based on a distributed extended state observer, and belongs to the field of aircraft formation control. In particular to a formation control method suitable for a 'collar-slave' type aircraft group, which ensures that the aircraft group flies according to a certain formation constraint, and the formation direction is kept consistent with the flight direction of a 'leader'.
Background
The problem of aircraft formation control is mainly to enable a plurality of aircraft to follow certain relative position constraints while flying. The usual formation control laws achieve the desired formation (the "lead-slave" formation control) by making the aircraft clusters fly following the "leader" and converging the relative positions between the aircraft to the desired values, mostly through positional information exchange between the aircraft. However, most formation control methods have a constant relative position between the aircraft or a variable relative position according to an artificially designed law, which results in the formation being able to translate in space or move according to an artificially designed law. In practice, the direction of the formation of the aircraft group is often consistent with the direction of flight of the "leader". The formation control method has larger access to the actual task requirements; while the actual mission obviously requires that the "follower" not only communicate positional information, but also acquire speed information of the "leader", this would increase the burden of communication between the aircraft.
In view of this, the invention designs an aircraft formation control method based on a distributed extended state observer, so that an aircraft group with a 'collar-slave' type structure flies according to a certain formation, and the direction of the formation is consistent with the flying direction of a 'leader', so that the aircraft group is relatively attached to an actual task. And each follower can estimate the position, the speed and the acceleration of the leader only by exchanging the position information, so that the communication resource is saved.
Disclosure of Invention
Aiming at the problem of formation control of 'leading-trailing' type aircrafts, the invention provides a formation control method, which ensures that an aircraft group flies according to a designated formation, and the direction of the formation is consistent with the flying direction of a 'leader'.
The technical conception of the invention is as follows: first, a coordinate system with consistent speed direction of the 'leader' is established, and a desired formation is designed in the coordinate system. Then designing a distributed extended state observer, wherein each follower can estimate the speed and acceleration of the leader only by exchanging the estimated value of the leader position with the neighbor; a coordinate transformation matrix is calculated according to the estimated values of the position and the speed of the leader, and the relative position relation in the expected formation is converted into the expected position of the follower in the inertia space. And finally, tracking the expected position by a follower through a certain position tracking control law so as to realize the expected formation.
The invention relates to an aircraft maneuvering formation control method based on a distributed extended state observer, which mainly comprises the following steps:
step 1, building an aircraft motion model
The aircraft group consists of a leader and N followers, and the kinematic equation of the leader is as follows:
wherein p is 0 ＝[x 0 ,y 0 ,z 0 ] T ，v 0 ＝[v x0 ,v y0 ,v z0 ] T And a 0 ＝[a x0 ,a y0 ,a z0 ] T The position, the speed and the acceleration of the leader in the three-dimensional space inertial coordinate system are respectively.
The motion model of the ith follower is:
wherein p is i ＝[x i ,y i ,z i ] T For the position of the ith follower in the inertial frame, V i ，θ i And psi is equal to i The speed of the ith follower, the ballistic dip angle and the ballistic deflection angle are respectively shown. Recording device g＝9.8m/s 2 Gravitational acceleration.
Step 2, estimating the position, the speed and the acceleration of the leader through a distributed extended state observer
The follower may obtain information from the neighbor and the leader may not obtain information from any follower. Ith follower pair p 0 ，v 0 And a 0 The estimated values of (c) are ζ respectively 1,i ，ζ 2,i And zeta 3,i And ζ is 1，0 ＝p 0 ，ζ 2,0 ＝v 0 ，ζ 3,0 ＝a 0 。
First, calculate the consistency error e of the ith follower with respect to the position estimation value c,i ：
Wherein,representing the neighbor set of the ith follower.
The distributed extended state observer is designed as follows:
wherein,for observer gain, sgn (·) represents the sign function.
Step 3, according to the estimated value zeta 2i Calculating affine transformation matrix L i
Defining affine transformation matrixWherein->In a ballistic coordinate systemRotating the matrix, and needing to be designed manually; l (L) r,i (ζ 2,i ) For the coordinate transformation matrix, expressed as:
wherein,to estimate zeta 2i ＝[ζ 2,i,x ,ζ 2,i,y ,ζ 2,i,z ] T Derived estimate of leader ballistics dip and ballistics deflection:
step 4, calculating the expected position p of the ith follower c,i
Defining a desired formation [ p ] in a leader ballistic coordinate system r,1 ,p r,1 ,...,p r,N ]，Is the desired relative position between the ith follower and the leader in the desired formation. Defining the expected position p in the inertial space of the ith follower c,i The method comprises the following steps:
p c,i ＝L i p r,i +ζ 1,i (7)
description: in the ideal expected position of the follower, L r,i The leader speed truth should be used, but the follower cannot obtain the leader speed truth, so the estimate is used. When the observer is stable, the speed estimated value is approximately equal to the actual value, so that the expected value of the follower position with relatively accurate position can be calculated by the distributed expansion state observer in the step 2.
Step 5, calculating the expected value of the position differential of the ith follower
Calculating the position error e of the ith follower p,i ：
e p,i ＝p i -p c,i (8)
Giving the expected value v of the position derivative of the ith follower c,i ＝[v c,i,x ,v c,i,y ,v c,i,z ] T ：
Wherein,for feedback gain->Is p c,i Approximately differential of +.>The differential filter gain is approximated.
Step 6, providing the formation maneuvering control law of the ith follower
Calculating the speed error e of the ith follower v,i ：
Wherein,to approximate differential filter gain +.>V is c,i Is a derivative of the approximation of (a).
Calculating acceleration command a under inertial coordinate system c,i ：
Wherein,is the feedback gain.
Giving a control law u i ＝[a V,i ,a θ,i ,a ψ,i ] T :
The invention has the beneficial effects that:
1. with the use of a distributed extended state observer, each follower can estimate the speed and acceleration information of the leader by only sharing an estimated value for the position of the leader with the neighbors.
2. The direction of the formation can be kept consistent with the direction of the leader's flight by defining the desired formation in the leader's ballistic coordinate system and then converting it to the desired position of each follower by affine transformation.
Description of the drawings:
fig. 1 is an aircraft group communication topology.
FIG. 2 is a schematic illustration of a formation.
Fig. 3 is a flight path of an aircraft fleet.
Fig. 4 shows the observer x-direction position observation error.
Fig. 5 shows the position observation error in the y direction of the observer.
Fig. 6 shows the position observation error in the z direction of the observer.
Fig. 7 shows the speed observation error in the x direction of the observer.
Fig. 8 shows the speed observation error in the y direction of the observer.
Fig. 9 shows the speed observation error in the z direction of the observer.
Fig. 10 shows the position error in the x direction.
Fig. 11 shows the position error in the y direction.
Fig. 12 shows the position error in the z direction.
Fig. 13 is a control input of the follower 1.
Fig. 14 is a control input of the follower 2.
Fig. 15 shows the control input of the follower 3.
Fig. 16 is a control input of the follower 4.
The specific embodiment is as follows:
the technical scheme and technical features of the present invention will now be further described based on the formation flight cases embodied in fig. 1-16.
An aircraft group consists of 1 leader with 5 followers, the communication topology in the group is shown in fig. 1. Node 0 is the leader, and the other nodes are the followers; directed edges connected to node 0 represent that the leader only sends information to nodes 1 and 2 without receiving information, and undirected edges between follower nodes represent that bidirectional communication is performed between followers.
The formation control tasks are as follows: and defining a formation in the direction of the flight speed of the leader, enabling the aircraft to fly along with the leader according to the formation, and completing the tracking control of the time-varying formation. The formation definition is shown in FIG. 2, where coordinate system OXYZ is the leader ballistic coordinate system. The relative positional relationship in the formation is as in formula (13):
and rotates the matrixAs in equation (14):
i.e. the formation is rotated around the OX axis by an angle y.
And verifying the formation control method by means of Matlb and Simulink. The motion trail of the leader is as shown in formula (15):
initial motion state of the aircraft group is as in table 1:
table 1 initial state of motion for a fleet of aircraft
The parameters of the distributed extended state observer and control law are designed as in table 2:
table 2 distributed extended state observer and control law parameter design
Defining a distributed extended state observer with respect to p 0 Is of the observed error epsilon p,i ＝[ε x,i ,ε y,i ,ε z,i ] T Concerning v 0 Is of the observed error epsilon v,i ＝[ε vx,i ,ε vy,i ,ε vz,i ] T And about a 0 Is of the observed error epsilon a,i ＝[ε ax,i ,ε ay,i ,ε az,i ] T ：
The respective observation error curves are shown in fig. 4 to 9. It can be seen that the position observation ζ is shared only with neighbors 1,i On the premise of the above, the observed errors on the position and the speed of the leader are fast converged, and the errors remain stable when the leader maneuvers. Position error e p,i ＝[e x,i ,e y,i ,e z,i ] T The curves are shown in FIGS. 10-12, control input u i 13-16, it can be seen that the control law can converge the position error so that the aircraft group meets the relative position relationship specified by the formation and controls the quantity inputWithin an acceptable range.
Claims (10)
1. The aircraft maneuvering formation control method based on the distributed extended state observer is characterized by comprising the following steps of:
step 1, establishing an aircraft motion model;
step 2, estimating the position, the speed and the acceleration of a leader through a distributed extended state observer;
step 3, according to the estimated value zeta 2i Calculating affine transformation matrix L i ；
Step 4, calculating the expected position p of the ith follower c,i ；
Step 5, calculating an expected value of the position derivative of the ith follower;
and 6, giving the formation maneuvering control law of the ith follower.
2. A method of controlling the maneuver formation of an aircraft based on a distributed extended state observer as defined in claim 1, wherein: in a first step of the process, the process is carried out,
the aircraft group consists of a leader and N followers, and the kinematic equation of the leader is as follows:
wherein p is 0 ＝[x 0 ,y 0 ,z 0 ] T ，v 0 ＝[v x0 ,v y0 ,v z0 ] T And a 0 ＝[a x0 ,a y0 ,a z0 ] T The position, the speed and the acceleration of the leader in the three-dimensional space inertial coordinate system are respectively.
3. A method of controlling the motoring of an aircraft based on a distributed extended state observer according to claim 1 or 2, characterized in that: the motion model of the ith follower is:
wherein p is i ＝[x i ,y i ,z i ] T For the position of the ith follower in the inertial frame, V i ，θ i And psi is equal to i The speed of the ith follower, the ballistic dip angle and the ballistic deflection angle are respectively; recording device g＝9.8m/s 2 Gravitational acceleration.
4. A method of controlling the maneuver formation of an aircraft based on a distributed extended state observer as defined in claim 1, wherein: in step 2, the follower obtains information from the neighbor and the leader does not obtain information from any follower; ith follower pair p 0 ，v 0 And a 0 The estimated values of (c) are ζ respectively 1,i ，ζ 2,i And zeta 3,i And ζ is 1,0 ＝p 0 ，ζ 2,0 ＝v 0 ，ζ 3,0 ＝a 0 。
5. A method of controlling the motoring of an aircraft based on a distributed extended state observer according to claim 1 or 4, wherein: calculating a consistency error e of the ith follower with respect to the position estimate c,i ：
Wherein,representing the neighbor set of the ith follower.
6. A method of aircraft maneuver formation control based on a distributed extended state observer as defined in claim 5 wherein: the distributed extended state observer is designed as follows:
wherein,for observer gain, sgn (·) represents the sign function.
7. A method of controlling the maneuver formation of an aircraft based on a distributed extended state observer as defined in claim 1, wherein: in step 3, an affine transformation matrix is definedWherein->Is a rotation matrix in a ballistic coordinate system; l (L) r,i (ζ 2,i ) For the coordinate transformation matrix, expressed as:
wherein,to estimate zeta 2i ＝[ζ 2,i,x ,ζ 2,i,y ,ζ 2,i,z ] T Derived estimate of leader ballistics dip and ballistics deflection:
8. a method of controlling the maneuver formation of an aircraft based on a distributed extended state observer as defined in claim 1, wherein: in step 4, the desired formation [ p ] is defined in the leader ballistic coordinate system r,1 ,p r,1 ,...,p r,N ]，A desired relative position between the ith follower and the leader in the desired formation; defining the expected position p in the inertial space of the ith follower c,i The method comprises the following steps:
p c,i ＝L i p r,i +ζ 1,i (7)。
9. a method of controlling the maneuver formation of an aircraft based on a distributed extended state observer as defined in claim 1, wherein: in step 5, the position error e of the ith follower is calculated p,i ：
e p,i ＝p i -p c,i (8)
Giving the expected value v of the position derivative of the ith follower c,i ＝[v c,i,x ,v c,i,y ,v c,i,z ] T ：
Wherein,for feedback gain->Is p c,i Approximately differential of +.>The differential filter gain is approximated.
10. A method of controlling the maneuver formation of an aircraft based on a distributed extended state observer as defined in claim 1, wherein: in step 6, the speed error e of the ith follower is calculated v,i ：
Wherein,to approximate differential filter gain +.>V is c,i Is a derivative of the approximation of (a);
calculating acceleration command a under inertial coordinate system c,i ：
Wherein,is the feedback gain;
giving a control law u i ＝[a V,i ,a θ,i ,a ψ,i ] T :
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| CN117873136B (en) * | 2024-03-11 | 2024-05-24 | 西北工业大学 | Control method for cooperative flight and collision prevention of preset performance of high-speed aircraft |
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