An aircraft formation control method based on a distributed extended state observer

Abstract

The application designs a kind of aircraft formation control method based on distributed extended state observer, to make aircraft group with "leader-follower" structure fly according to expected formation.The method first estimates the position and speed information of leader by distributed extended state observer for all followers.Then, the coordinate transformation matrix is calculated according to the speed estimation value, and the expected position of follower in inertial space is calculated according to the coordinate transformation matrix and the position estimation value.Finally, the expected position is tracked by the position tracking control law to control the follower, so as to realize the expected formation.In the method, the information interaction between each follower only involves the estimated value of the leader position, and the formation direction is consistent with the flight direction of the leader.

Description

Technical Field

[0001] This invention designs an aircraft maneuver formation control method based on a distributed extended state observer, belonging to the field of aircraft formation control. Specifically, it invents a formation control method suitable for "leader-follower" type aircraft groups, enabling the aircraft group to fly according to certain formation constraints, with the formation direction consistent with the flight direction of the "leader". Background Technology

[0002] The main problem in aircraft formation control is ensuring that multiple aircraft adhere to certain relative position constraints during flight. Common formation control laws mostly rely on the exchange of position information between aircraft to guide the swarm to follow a "leader" and converge the relative positions of each aircraft to a desired value, achieving a desired formation ("leader-follower" formation control). However, in most formation control methods, the relative positions between aircraft are either constants or variables that vary according to a pre-designed pattern. This means the formation can only translate or move according to a pre-designed pattern in space. In actual missions, the orientation of the aircraft swarm's formation often needs to be consistent with the flight direction of the "leader." The aforementioned formation control methods deviate significantly from the requirements of actual missions; and actual missions clearly require "followers" to not only exchange position information but also obtain the "leader's" velocity information, which increases the communication burden between aircraft.

[0003] In view of this, this invention designs an aircraft formation control method based on a distributed extended state observer, enabling an aircraft group with a "leader-follower" structure to fly in a certain formation, with the formation direction consistent with the flight direction of the "leader," which closely matches the actual mission. Furthermore, each "follower" only needs to exchange position information to estimate the position, velocity, and acceleration of the "leader," saving communication resources. Summary of the Invention

[0004] This invention addresses the problem of "leader-follower" aircraft formation control by proposing a formation control method that enables the aircraft group to fly in a designated formation, with the formation direction consistent with the flight direction of the "leader".

[0005] The technical concept of this invention is as follows: First, a coordinate system is established with the velocity direction aligned with that of the "leader," and the desired formation is designed within this coordinate system. Then, a distributed extended state observer is designed, allowing each "follower" to estimate the "leader's" velocity and acceleration simply by exchanging estimates of the "leader's" position with its neighbors. Based on these estimates, a coordinate transformation matrix is ​​calculated, converting the relative positional relationships within the desired formation into the desired positions of the "followers" in inertial space. Finally, a specific position tracking control law enables the "followers" to track the desired positions, thereby achieving the desired formation.

[0006] This invention discloses an aircraft maneuver formation control method based on a distributed extended state observer, the main steps of which are as follows:

[0007] Step 1. Establish the aircraft motion model

[0008] The swarm of aircraft consists of one leader and N followers. The kinematic equation of the leader is:

[0009]

[0010] Where p0 = [x0, y0, z0] T v0 = [v x0 ,v y0 ,v z0 ] T with a0=[a x0 ,a y0 ,a z0 ] T These represent the leader's position, velocity, and acceleration in a three-dimensional inertial coordinate system.

[0011] The motion model of the i-th follower is:

[0012]

[0013] Where, p i =[x i ,y i ,z i ] T Let V be the position of the i-th follower in the inertial coordinate system. i θ i With ψ i Let be the velocity magnitude, trajectory inclination angle, and trajectory deviation angle of the i-th follower, respectively. g = 9.8 m / s 2 This is the acceleration due to gravity.

[0014] Step 2. Estimate the leader's position, velocity, and acceleration using a distributed extended state observer.

[0015] Followers can obtain information from their neighbors, while leaders do not obtain information from any followers. The i-th follower's estimates of p0, v0, and a0 are ζ, respectively. 1,i , ζ 2,i and ζ 3,i , and ζ 1，0 =p0, ζ 2,0 =v0,ζ 3,0 =a0.

[0016] First, calculate the consensus error e of the i-th follower regarding the position estimate. c,i:

[0017]

[0018] in, Let represent the set of neighbors of the i-th follower.

[0019] The distributed extended state observer is designed as follows:

[0020]

[0021] in, Let sgn(·) be the observer gain, and let sgn(·) denote the sign function.

[0022] Step 3. Based on the estimated value ζ 2i Calculate the affine transformation matrix L i

[0023] Define the affine transformation matrix in The rotation matrix in the ballistic coordinate system needs to be designed manually; L r,i (ζ 2,i ) is the coordinate transformation matrix, represented as:

[0024]

[0025] in, For the estimated value ζ 2i =[ζ 2,i,x ,ζ 2,i,y ,ζ 2,i,z ] T The derived estimates of the leader ballistic inclination angle and ballistic deflection angle are as follows:

[0026]

[0027] Step 4. Calculate the expected position p of the i-th follower. c,i

[0028] Define the desired formation in the leader's ballistic coordinate system [p] r,1 ,p r,1 ,...,p r,N ], Let p be the expected relative position between the i-th follower and the leader in the desired formation. Let p be the expected position p of the i-th follower in inertial space. c,i for:

[0029] p c,i =L i p r,i +ζ 1,i (7)

[0030] Note: In the ideal expected position of followers, L r,i The true velocity of the leader should be used, but the followers cannot obtain the true velocity of the leader, so the estimated value is used. When the observer is stable, the velocity estimate is approximately equal to the actual value, so the expected value of the follower's position can be calculated more accurately using the distributed extended state observer in step 2.

[0031] Step 5. Calculate the expected value of the differential of the position of the i-th follower.

[0032] Calculate the positional error e of the i-th follower. p,i :

[0033] e p,i =p i -p c,i (8)

[0034] Give the expected value v of the differential of the position of the i-th follower. c,i =[v c,i,x ,v c,i,y ,v c,i,z ] T :

[0035]

[0036] in, For feedback gain, For p c,i The approximate differential, Approximate differential filter gain.

[0037] Step 6. Give the formation maneuver control law for the i-th follower.

[0038] Calculate the velocity error e of the i-th follower. v,i :

[0039]

[0040] in, For approximate differential filter gain, For v c,i The approximate differential.

[0041] The command 'a' is used to calculate acceleration in the inertial coordinate system. c,i :

[0042]

[0043] in, For feedback gain.

[0044] Give the control law u i =[a V,i ,a θ,i,a ψ,i ] T :

[0045]

[0046] The beneficial effects of this invention are as follows:

[0047] 1. A distributed extended state observer is used, where each follower only needs to share the estimated position of the leader with its neighbors to estimate the leader's velocity and acceleration information.

[0048] 2. Define the desired formation in the leader's ballistic coordinate system, and then transform it into the desired position of each follower through affine transformation, so that the formation direction is consistent with the leader's flight direction. Attached image description:

[0049] Figure 1 This is the communication topology for a group of aircraft.

[0050] Figure 2 This is a diagram illustrating the formation of the formation.

[0051] Figure 3 The flight path of the aircraft group.

[0052] Figure 4 The x-direction position observation error of the observer.

[0053] Figure 5 The position observation error of the observer in the y-direction is denoted as .

[0054] Figure 6 This represents the position observation error of the observer in the z-direction.

[0055] Figure 7 The velocity observation error in the x-direction of the observer is denoted as .

[0056] Figure 8 The velocity observation error in the y-direction of the observer is denoted as .

[0057] Figure 9 The velocity observation error in the z-direction of the observer is denoted as .

[0058] Figure 10 This represents the positional error in the x-direction.

[0059] Figure 11 This represents the positional error in the y-direction.

[0060] Figure 12 This represents the position error in the z-direction.

[0061] Figure 13 For the control input of follower 1.

[0062] Figure 14For the control input of follower 2.

[0063] Figure 15 For the control input of follower 3.

[0064] Figure 16 For the control input of follower 4. Detailed implementation method:

[0065] Now based on the appendix Figure 1-16 The formation flight examples illustrate the technical solution and features of this invention.

[0066] The aircraft swarm consists of one leader and five followers. The communication topology within the swarm is as follows: Figure 1 As shown, node 0 is the leader, and the other nodes are followers; the directed edges connected to node 0 represent that the leader only sends messages to nodes 1 and 2 and does not receive messages, while the undirected edges between follower nodes represent bidirectional communication between followers.

[0067] The formation control task is to define a formation in the direction of the leader's flight speed, and then have the aircraft follow the leader according to that formation, thus completing the tracking control of a time-varying formation. The formation definition is as follows: Figure 2 As shown, the coordinate system OXYZ is the leader's ballistic coordinate system. The relative positional relationships in the formation are as shown in formula (13):

[0068]

[0069] And rotation matrix As in formula (14):

[0070]

[0071] That is, the formation rotates around the OX axis by an angle γ.

[0072] The above formation control method was verified using Matlb and Simulink. The leader's trajectory is shown in equation (15):

[0073]

[0074] The initial motion state of the aircraft swarm is shown in Table 1:

[0075] Table 1 Initial Motion State of the Aircraft Swarm

[0076]

[0077]

[0078] The parameter design of the distributed extended state observer and control law is shown in Table 2:

[0079] Table 2. Parameter Design of Distributed Extended State Observer and Control Law

[0080]

[0081] Define the observation error ε of the distributed extended state observer with respect to p0. p,i =[ε x,i ,ε y,i ,ε z,i ] T The observation error ε regarding v0 v,i =[ε vx,i ,ε vy,i ,ε vz,i ] T and the observation error ε with respect to a0 a,i =[ε ax,i ,ε ay,i ,ε az,i ] T :

[0082]

[0083] The observation error curves are as follows Figure 4-9 As shown. It can be seen that when only sharing location observations ζ with neighbors... 1,i Under the premise that the observation errors regarding the leader's position and velocity converge rapidly, and remain stable during the leader's maneuver, the position error e is given. p,i =[e x,i ,e y,i ,e z,i ] T Curves Figure 10-12 As shown, the control input u i Curves Figure 13-16 As shown, the control law can bring the position error to converge, thereby enabling the aircraft group to meet the relative positional relationship specified in the formation, and the control input is within an acceptable range.

Claims

1. A method for aircraft maneuver formation control based on a distributed extended state observer, characterized in that, The steps include the following: Step 1. Establish a motion model of the aircraft; Step 2. Estimate the leader's position, velocity, and acceleration using a distributed extended state observer; each follower only needs to share the leader's position estimate with its neighbors to estimate the leader's velocity and acceleration information; followers obtain information from their neighbors, while the leader does not obtain information from any followers; Followers , and The estimated values ​​are respectively , and ,and , , ; Step 3. Based on the estimated value Calculate the affine transformation matrix ; Step 4. Calculate the first... The expected position of the followers ; Step 5. Calculate the first... The expected value of the differential of the position of a follower; Step 6. Give the first The formation maneuver control law of the followers; Among them, the calculation of the first Consistency error among followers regarding position estimates : (3) in, Indicates the first The neighborhood of the followers; The distributed extended state observer is designed as follows: (4) in, For observer gain, Represents a symbolic function; Define the affine transformation matrix ,in This is the rotation matrix in the ballistic coordinate system; The coordinate transformation matrix is ​​represented as: (5) in, , For the estimated value The derived estimates of the leader ballistic inclination angle and ballistic deflection angle are as follows: (6)； Define the desired formation in the leader ballistic coordinate system , For the desired formation The expected relative position between followers and leaders N Let there be N followers; define the first... The expected position of the followers in the inertial space for: (7)。 2. The aircraft maneuver formation control method based on a distributed extended state observer according to claim 1, characterized in that: In step one, The aircraft group is led by a leader and The leader is composed of followers, and the kinematic equation of the leader is: (1) in, , and These represent the leader's position, velocity, and acceleration in a three-dimensional inertial coordinate system.

3. The aircraft maneuver formation control method based on a distributed extended state observer according to claim 1 or 2, characterized in that: No. The motion model of the followers is as follows: (2) in, For the first The position of each follower in the inertial coordinate system. , and The first The speed, trajectory inclination, and trajectory deviation of the follower; [record / describe] , This is the acceleration due to gravity.

4. The aircraft maneuver formation control method based on a distributed extended state observer according to claim 3, characterized in that: In step 5, calculate the first The positional error of the followers : (8) Give the first Expected value of the differential of the position of the number of followers : (9) in, For feedback gain, for The approximate differential, Approximate differential filter gain.

5. The aircraft maneuver formation control method based on a distributed extended state observer according to claim 3, characterized in that: In step 6, calculate the first The speed error of the followers : (10) in, For approximate differential filter gain, for The approximate differential; Calculate acceleration command in inertial coordinate system : (11) in, For feedback gain; Give the control law : (12) in, and The first The trajectory inclination and trajectory deflection of the followers.

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