Multi-aircraft control-limited cooperative formation method based on distributed observer

Abstract

The application designs a multi-aircraft control limited cooperative formation method based on a distributed observer, so that a group of aircrafts with a "leader-follower" structure generates a specified formation in a limited time. The method first makes all followers obtain the position information of the leader through a distributed observer, and calculates the position expectation of the follower. Then, the position error and the expected velocity vector of the follower are calculated, and finally, the velocity error of the follower is calculated, and the overload instruction required by the follower is calculated according to the control law. In the method, the information interaction between the aircrafts only involves the position information, and the amplitude of the overload instruction has a clear upper limit. The application enables the aircraft group to generate formation instructions based on the position of the leader, and makes the position error of the follower converge in a limited time under the condition that the control amount input is limited.

Description

Technical Field

[0001] This invention relates to an aircraft formation control method based on a distributed observer, belonging to the field of aircraft formation control. Specifically, it is a multi-aircraft control constrained cooperative formation method based on a distributed observer, which enables the aircraft group to generate formation commands based on the position of the leader, and enables the position errors of the followers to converge in a finite time under limited control input. Background Technology

[0002] The main problem of aircraft formation control is to enable multiple aircraft to form and maintain a certain relative positional configuration in space to achieve better mission performance. Consistency control theory is a commonly used control theory in formation control, primarily aiming to achieve the desired relative positions by ensuring the stable convergence of consistency errors related to the relative positions and velocities of the aircraft. However, formation consistency control methods typically require the simultaneous use of both aircraft velocity and position information, and precise formation generation often results in significant control inputs. Therefore, this invention proposes a multi-aircraft controlled constrained cooperative formation method based on distributed observers. This method enables a group of aircraft with a "leader-follower" structure to generate the desired formation configuration within a finite time. In this method, information exchange between aircraft involves only positional information, and the control inputs of each aircraft have clear upper bounds. Summary of the Invention

[0003] This invention addresses the formation control problem of "leader-follower" aircraft swarms by proposing a multi-aircraft control constrained cooperative formation method based on distributed observers, enabling the aircraft swarm to generate a specified formation within a finite time.

[0004] The technical concept of this invention is as follows: First, a distributed observer is designed to enable followers in a swarm of aircraft to observe the position of the leader, and to generate position commands for the followers based on the observed position of the leader and the desired formation. Then, a position tracking algorithm for the followers is designed to enable them to track the leader's position commands, thereby enabling the swarm to generate the desired formation.

[0005] This invention provides a multi-aircraft control-constrained cooperative formation method based on distributed observers, which specifically includes the following steps.

[0006] Step 1: Establish a motion model of the aircraft;

[0007] In three-dimensional space, the first The motion model of a follower aircraft is described by equation (1).

[0008] (1)

[0009] .in, This represents the position of the follower in three-dimensional space. for The differential; The three elements are the follower's flight speed, trajectory inclination angle, and trajectory deviation angle; For the overload of the follower; and Represent The input matrix and the gravitational acceleration The impact of this is calculated as follows:

[0010]

[0011] and The conversion relationship is shown in equation (2):

[0012] (2)

[0013] Step 2: Observe the spatial location of the leader using distributed observers;

[0014] First, it is agreed that, for and ,have:

[0015]

[0016]

[0017] No. One follower for the leader's position The observed value is The method for calculating the observed values ​​is shown in equation (3);

[0018] (3)

[0019] This invention does not require the initial values ​​of the observations to be bounded real numbers. In equation (3), the positive constants... and This is the gain coefficient, a positive constant greater than 1. The power coefficient is... It is a positive constant; The consistency error of the location observations is calculated as shown in equation (4):

[0020] (4)

[0021] in, It is the first The observations of the leader's position by each follower. Recorded as the number Observer error of each follower .

[0022] In equation (4), It is the first There exists a communication coefficient between the j-th follower and the j-th follower, satisfying:

[0023]

[0024] It is the first There exists a communication coefficient between each follower and leader, satisfying:

[0025]

[0026] Step 3: Calculate the followers' desired positions;

[0027] Based on the measured values ​​obtained in step 2 , No. Each follower calculates their desired position. ,Right now

[0028] (5)

[0029] in, For the first The expected relative displacement between followers and leaders.

[0030] Step 4: Calculate the positional error variable of the follower;

[0031] Definition of the first The positional error of each follower is The calculation method is shown in equation (6).

[0032] (6)

[0033] Step 5: Calculate the expected value of the position derivative;

[0034] No. The expected value of the differential of each follower position is ; The calculation method is shown in equation (7):

[0035] (7)

[0036] in, The calculation method is shown in equation (8).

[0037] (8)

[0038] In equations (7) and (8), , , , and All are positive definite real diagonal matrices; and Given a positive real number, the requirement is... and satisfy:

[0039]

[0040] The differential of position according to the expected value When changes occur, positional error can be achieved. The convergence time of the largest position error among all followers is finite. Represented as:

[0041]

[0042] in, It is the maximum value of the initial position error of each follower minus the square of the norm; and It is a bounded positive real number.

[0043] Step 6: Calculate the velocity error variable of the follower;

[0044] First, calculate the first equation based on equations (2) and (7). The speed of each follower Ballistic inclination angle with ballistic deflection Expected value , and ,Right now,

[0045] (9)

[0046] Then calculate the first... The speed error of each follower As shown in equation (10):

[0047] (10)

[0048] in, and Representing the first The trajectory angle of the follower Ballistic deflection The difference between it and its expected value; Based on the The flight speed of the followers Variables defined to account for the difference between their instruction values ​​are used to guarantee , and These represent the upper and lower limits of the flight speed of group members, respectively.

[0049] Step 7: Describe the formation control law for generating formations in a finite time;

[0050] The control law controls the quantity Designed as follows:

[0051] (11)

[0052] in, , , and All are positive definite real diagonal matrices; and It is a positive real number.

[0053] In equation (11) and Represent The input matrix and the effect of gravitational acceleration on it. The calculation method is shown in equation (12):

[0054] (12)

[0055] In equation (11) , The notation for elements in a medium is as follows:

[0056]

[0057] but When designing according to equation (11), the upper bound of the control quantity can satisfy the following constraint:

[0058]

[0059] Simultaneously, this control quantity can achieve speed error... Finite-time convergence. The convergence time of the velocity error of each follower. Represented as:

[0060]

[0061] in, It is the maximum value of the initial value of the velocity error of each follower minus the square of the 2-norm; and It is a bounded positive real number.

[0062] The advantages and beneficial effects of this invention are as follows:

[0063] 1. A swarm of aircraft can generate the desired formation within a finite time.

[0064] This invention enables both velocity and position errors to converge in a finite time. Once both errors have converged, the aircraft swarm can be considered to have generated the desired formation. The maximum time required for the aircraft swarm to generate the formation is [not specified]. for:

[0065]

[0066] 2. The control input (overload) has a clear upper limit.

[0067] 3. The information exchange between aircraft only involves location information. Attached Figure Description

[0068] Figure 1 This is the communication topology for aircraft groups.

[0069] Figure 2 For distributed observers in The curve showing the change in observer error in the direction.

[0070] Figure 3 For distributed observers in The curve showing the change in observer error in the direction.

[0071] Figure 4 For distributed observers in The curve showing the change in observer error in the direction.

[0072] Figure 5 For 5 followers Position error variation curve in the direction.

[0073] Figure 6 For 5 followers Position error variation curve in the direction.

[0074] Figure 7 For 5 followers Position error variation curve in the direction.

[0075] Figure 8 The overload command change curve for the first follower.

[0076] Figure 9 The overload command change curve for the second follower.

[0077] Figure 10 The overload command change curve for the third follower.

[0078] Figure 11 The overload command change curve for the 4th follower.

[0079] Figure 12 The overload command change curve for the 5th follower. Detailed Implementation

[0080] Now based on the appendix Figure 1-12 The formation flight examples illustrate the technical solution and features of this invention.

[0081] The aircraft group consists of The group consists of one leader and five followers. The communication topology within the group is as follows: Figure 1 As shown (where node 0 represents the leader, and nodes 1 to 5 represent followers). The group control task is: to make the group consist of... Figure 2 The state shown becomes Figure 3 The state shown indicates that a specified formation has been formed.

[0082] The designed formation control algorithm was verified using Matlab and Simulink. The leader's flight trajectory is described by equation (13):

[0083] (13)

[0084] The initial position of the aircraft group is: in meters.

[0085]

[0086] Calculate the expected formation of the group based on observations of the leader's position: in meters.

[0087]

[0088] The observer parameters are shown in equation (14):

[0089] (14)

[0090] in, It represents a 3D identity matrix.

[0091] The control law parameters are shown in equation (15):

[0092] (15)

[0093] The simulation control law takes effect after 0.75s so that the observer error can fully converge and the variables in equation (8) can enter the ideal state. Figures 2 to 4 This demonstrates that the observation error of the distributed observer can converge rapidly to near zero within a short, finite time. Figures 5 to 7 This demonstrates that the three-dimensional spatial position error of each follower can converge to near 0 within a finite time. Figures 8 to 12 Explain the overload instructions for each follower. , and The values ​​do not exceed 6.1, 7.1 and 6.1 respectively, which are in line with the theoretically derived upper bound constraints of the control quantity.

Claims

1. A multi-aircraft control-constrained cooperative formation method based on distributed observers, characterized in that: The specific steps are as follows: Step 1: Establish a motion model of the aircraft; In three-dimensional space, the first The motion model of the follower aircraft is described by equation (1); （1） ;in This represents the position of the follower in three-dimensional space. for The differential; The three elements are the follower's flight speed, trajectory inclination angle, and trajectory deviation angle; For the overload of the follower; and Represent The input matrix and the gravitational acceleration The impact; and The conversion relationship is shown in equation (2): （2） Step 2: Observe the spatial location of the leader using distributed observers. First, it is agreed that, for and ,have: ； ； No. One follower for the leader's position The observed value is The method for calculating the observed values ​​is shown in equation (3); （3） In equation (3), positive constants and This is the gain coefficient, a positive constant greater than 1. The power coefficient is... It is a positive constant; This refers to the consistency error of the location observations; Step 3: Calculate the followers' desired position Based on the measured values ​​obtained in step 2 , No. Each follower calculates their desired position. ,Right now: （5） in For the first The expected relative displacement between followers and leaders; Step 4: Calculate the positional error variable of the follower Definition of the first The positional error of each follower is The calculation method is shown in equation (6): （6） Step 5: Calculate the expected value of the position derivative. No. The expected value of the differential of each follower position is ; The calculation method is shown in equation (7): （7） in The calculation method is shown in equation (8); （8） In equations (7) and (8), , , , and All are positive definite real diagonal matrices; and Given a positive real number, the requirement is... and satisfy: ； Step 6: Calculate the velocity error variable of the follower. First, calculate the first equation based on equations (2) and (7). The speed of each follower Ballistic inclination angle with ballistic deflection Expected value , and ,Right now: （9） Then calculate the first... The speed error of each follower As shown in equation (10): （10） in, and Representing the first The trajectory angle of the follower Ballistic deflection The difference between it and its expected value; Based on the The flight speed of the followers Variables defined to account for the difference between their instruction values ​​are used to guarantee , and These are the upper and lower limits of the flight speed of the group members, respectively; Step 7: Describe the formation control law for generating formations in a finite time. The control law controls the quantity Designed as follows: （11） in, , , and All are positive definite real diagonal matrices; and It is a positive real number; In equation (11) and Represent The input matrix and the effect of gravitational acceleration on it; its calculation method is shown in equation (12): （12） In equation (11) , The notation for elements in a medium is as follows: ； but When designing according to equation (11), the upper bound of the control quantity should satisfy the following constraint: ； Simultaneously, this control quantity achieves speed error. Finite-time convergence; convergence time of velocity error for each follower Represented as: ； in It is the maximum value of the initial value of the velocity error of each follower minus the square of the norm; and It is a bounded positive real number.

2. The multi-aircraft control-constrained cooperative formation method based on distributed observers according to claim 1, characterized in that: In step 1, and Represent The input matrix and the gravitational acceleration The impact of this is calculated as follows: 。 3. The multi-aircraft control-constrained cooperative formation method based on distributed observers according to claim 1, characterized in that: In step 2, the initial values ​​of the observations are not required; they can simply be bounded real numbers.

4. The multi-aircraft control-constrained cooperative formation method based on distributed observers according to claim 1, characterized in that: In step 2, The calculation method is shown in equation (4): （4） in It is the first The observations of the leader's position by each follower; Recorded as the number Observer error of each follower ; It is the first There exists a communication coefficient between the j-th follower and the j-th follower. It is the first The communication coefficient exists between each follower and leader.

5. The multi-aircraft control-constrained cooperative formation method based on distributed observers according to claim 4, characterized in that: In step 2, in equation (4), It is the first There exists a communication coefficient between the j-th follower and the j-th follower, satisfying: ； It is the first There exists a communication coefficient between each follower and leader, satisfying: 。 6. The multi-aircraft control-constrained cooperative formation method based on distributed observers according to claim 1, characterized in that: In step 5, the derivative of the position is calculated according to the expected value. When changes occur, position error is achieved. Finite-time convergence; the convergence time of the largest position error among all followers. Represented as: ； in It is the maximum value of the initial position error of each follower minus the square of the norm; and It is a bounded positive real number.

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