Triggering type multi-aircraft cooperative guidance algorithm for maneuvering target

Abstract

The invention discloses a maneuvering target-oriented trigger type multi-aircraft cooperative guidance algorithm. The algorithm comprises the following steps of establishing a relative kinematics model of multiple aircrafts and a maneuvering target; based on the kinematics model, cooperative guidance laws capable of enabling state variables to converge consistently in fixed time are designed in a sight line tangential channel and a sight line normal channel respectively; an interference observer is arranged to estimate and compensate system interference in the cooperative guidance law; and the aircraft flies according to the cooperative guidance law after the system disturbance is compensated. According to the maneuvering target-oriented triggered multi-aircraft cooperative guidance algorithm disclosed by the invention, the guidance error can obtain a faster convergence speed, and the upper bound of the convergence time of the guidance error is not influenced by initial conditions, so that the communication burden can be effectively reduced, and the cooperative efficiency is improved.

Description

[0001] The application relates to a trigger type multi-aircraft cooperative guidance algorithm for a mobile target and belongs to the technical field of aircraft control. BACKGROUND

[0002] Multi-aircraft time and space cooperation can realize multi-directional simultaneous arrival of a target, which has important practical significance for aerial recovery and encirclement of unmanned aircraft.

[0003] Since the cooperative guidance method using neighborhood communication needs continuous information interaction between aircrafts, a large communication burden is caused in actual engineering; meanwhile, the existing cooperative method mostly adopts gradual convergence, and it is difficult to meet the requirement of rapid convergence of guidance error.

[0004] Therefore, it is necessary to further study the existing multi-aircraft cooperative guidance method to solve the above problems. SUMMARY

[0005] In order to overcome the above problems, the application is proposed after deep research, and a trigger type multi-aircraft cooperative guidance algorithm for a mobile target is provided, which comprises the following steps:

[0006] S1, establishing a relative kinematic model of multi-aircraft and a mobile target;

[0007] S2, based on the kinematic model, designing a cooperative guidance law capable of making state quantities converge uniformly in a fixed time in two channels of line-of-sight tangent and line-of-sight normal;

[0008] S3, setting an interference observer to estimate and compensate system interference in the cooperative guidance law;

[0009] S4, flying the aircraft with the cooperative guidance law after compensation of system disturbance.

[0010] In a preferred embodiment, the relative kinematic model of multi-aircraft and a mobile target is expressed as:

[0011]

[0012] Wherein, r i represents the distance between the aircraft M i and the target T, V mi represents the speed of the aircraft M i , V t represents the speed of the target, q i represents the line-of-sight angle of the aircraft M i , gamma mi represents the trajectory deflection angle of the aircraft M i , gamma t represents the trajectory deflection angle of the target, and a mi represents the acceleration of the aircraft Mi the normal acceleration of the target, a t the normal acceleration of the target, a vi the tangential acceleration of the vehicle M i

[0013] Based on the relative kinematic model, the acceleration components in the line-of-sight tangential and normal directions are obtained, denoted as:

[0014]

[0015] where u ri is the acceleration component in the line-of-sight tangential direction, and u qi is the acceleration component in the line-of-sight normal direction, denoted as:

[0016] u ri = a vi cos(q i - γ mi ) + a mi sin(q i - γ mi )

[0017] u qi = -a vi sin(q i - γ mi ) + a mi cos(q i - γ mi ).

[0018] In a preferred embodiment, in S2, the design of the cooperative guidance law in the line-of-sight tangential direction includes the following sub-steps:

[0019] S211, set multi-vehicle constraints to achieve cooperative arrival of multiple vehicles to the target;

[0020] S212, set a control protocol to achieve fixed-time consensus of arrival time based on an event-triggered mechanism;

[0021] S213, add measurement errors in the control protocol;

[0022] S214, set an event-triggered function based on the multi-vehicle constraints and the control protocol to obtain the cooperative guidance law in the line-of-sight tangential direction.

[0023] In a preferred embodiment, in S211, the multi-vehicle constraints are denoted as:

[0024]

[0025] where t goi denotes the vehicle M i ​the remaining flight time of the aircraft M goj the remaining flight time of the aircraft M j the remaining flight time of the aircraft M fi the total flight time of the aircraft M i the total flight time of the aircraft M di the desired line-of-sight angle of the aircraft M i the desired line-of-sight angle of the aircraft M

[0026] In a preferred embodiment, the control protocol with measurement error is represented as:

[0027]

[0028] where e i (t) is the measurement error, which is set as:

[0029]

[0030] where, the control protocol of the aircraft M i , c1, c2, c3 are control gain parameters, and a is a constant parameter greater than 1, the last event trigger time k of the aircraft M i .

[0031] In a preferred embodiment, in S214, the event trigger function g i (t) is set as:

[0032]

[0033] where η ∈ (0, 1) is a constant parameter.

[0034] In a preferred embodiment, the cooperative guidance law u ri in the line-of-sight tangent direction is represented as:

[0035]

[0036] where, represents the external disturbance of the system.

[0037] In a preferred embodiment, in S2, the design of the cooperative guidance law in the line-of-sight normal direction includes the following sub-steps:

[0038] S221, set the guidance model in the line-of-sight normal direction;

[0039] S222, set the fixed-time convergent non-singular terminal sliding mode variable with all aircrafts being able to intercept the target at different angles as the guidance target;

[0040] S223, obtaining the cooperative guidance law of the line-of-sight normal channel based on the guidance model and the sliding mode variable.

[0041] In a preferred embodiment, in S221, the guidance model is set as:

[0042]

[0043] wherein ε qi , d qi are intermediate variables, ε qi =q i -q di , d qi =a t cos(q i -γ t ) / r i .

[0044] In a preferred embodiment, in S222, the fixed-time convergent non-singular terminal sliding mode variable is expressed as:

[0045]

[0046] wherein s i represents the sliding surface, and β q1 , β q2 , α q1 , α q2 are constant parameters.

[0047] The present application has the beneficial effects including:

[0048] (1) Compared with the cooperative control method of continuous communication, the method in the present application can effectively reduce the update frequency of the cooperative control quantity, and effectively reduce the working burden of the actuator;

[0049] (2) The guidance error can obtain a faster convergence speed, and the upper bound of the convergence time of the guidance error is not affected by the initial condition;

[0050] (3) The proposed fixed-time triggered cooperative guidance law can effectively reduce the communication burden and improve the cooperative efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 Fig. 1 shows a flowchart of the triggered multi-aircraft cooperative guidance algorithm for a maneuvering target according to a preferred embodiment of the present application;

[0052] Figure 2 Fig. 4 shows the observer error in Example 1;

[0053] Figure 3 Fig. 6 shows the aircraft motion trajectory in the horizontal plane in Example 1;

[0054] Figure 4 Aircraft remaining flight time in Example 1 is shown;

[0055] Figure 5 Aircraft line-of-sight angle in Example 1 is shown;

[0056] Figure 6 Aircraft-target line-of-sight angle rate in Example 1 is shown;

[0057] Figure 7 Aircraft overload command in Example 1 is shown. DETAILED DESCRIPTION

[0058] The application is further described in detail by the accompanying drawings and examples. The features and advantages of the present application will become more apparent from the detailed description, accompanying drawings, and claims.

[0059] The term "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any implementation described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other implementations. Unless specifically indicated otherwise, the drawings are not necessarily to scale.

[0060] The present application provides a trigger-type multi-UAV cooperative guidance algorithm for a maneuvering target, as shown in the following steps: Figure 1

[0061] S1, a relative kinematic model of the multi-UAV and the maneuvering target is established;

[0062] S2, based on the kinematic model, cooperative guidance laws are designed in the line-of-sight tangential and line-of-sight normal channels respectively, which can make the state quantities converge consistently within a fixed time;

[0063] S3, an interference observer is set to estimate and compensate the system interference in the cooperative guidance law;

[0064] S4, the UAV flies with the cooperative guidance law after compensating the system disturbance.

[0065] In S1, the relative kinematic model of the multi-UAV and the maneuvering target is expressed as:

[0066]

[0067] wherein r i represents the distance between the UAV M i and the target T, V mi represents the speed of the UAV M i , V t represents the speed of the target, q i represents the flight direction of the UAV M i ​the line-of-sight angle of the aircraft M mi denotes the ballistic angle of the aircraft M i a t denotes the ballistic angle of the target mi denotes the normal acceleration of the aircraft M i a t denotes the normal acceleration of the target vi denotes the tangential acceleration of the aircraft M i .

[0068] Further, the first two equations of the relative kinematic model are differentiated to obtain the acceleration components in the line-of-sight tangential and normal directions, denoted as

[0069]

[0070] where u ri is the acceleration component in the line-of-sight tangential direction, and u qi is the acceleration component in the line-of-sight normal direction, denoted as

[0071] u ri = a vi cos (q i - y mi ) + a mi sin (q i - y mi )

[0072] u qi = -a vi sin (q i - y mi ) + a mi cos (q i - y mi ).

[0073] In S2, the design of the cooperative guidance law in the line-of-sight tangential direction includes the following sub-steps:

[0074] S211, set a multi-aircraft constraint to achieve cooperative arrival of multiple aircrafts to the target;

[0075] S212, set a control protocol to achieve fixed-time consensus of arrival time based on an event-triggered mechanism;

[0076] S213, add measurement error in the control protocol;

[0077] S214, set an event-triggered function based on the multi-aircraft constraint and the control protocol to obtain the cooperative guidance law in the line-of-sight tangential direction.

[0078] In S211, the multi-aircraft constraint is denoted as

[0079]

[0080] where t goi represents the remaining flight time of the aircraft M i , t goj represents the remaining flight time of the aircraft M j , t fi represents the total flight time of the aircraft M i , q di represents the desired line-of-sight angle of the aircraft M i .

[0081] Further, the remaining flight time can be represented as:

[0082]

[0083] Differentiating it, we can obtain:

[0084]

[0085] d ri = a t sin(q i - γ t )

[0086] Further, since t fi = t + t goi , we can obtain from the above formula:

[0087]

[0088] where t is the time elapsed since the aircraft is launched, d′ ri is an intermediate variable.

[0089] The control protocol described in S212 is set as:

[0090]

[0091] where, represents the control protocol of the aircraft M i , c1, c2, c3 are control gain parameters, which are positive numbers, and α is a constant parameter greater than 1, represents the most recent event trigger time k of the aircraft M i , and satisfies

[0092] In S213, by setting a measurement error, a faster convergence speed can be obtained, and the upper bound of the convergence time is not affected by the initial condition, thereby effectively reducing the communication burden and improving the coordination efficiency.

[0093] Preferably, the measurement error ei (t) is:

[0094]

[0095] The control protocol with measurement error can be expressed as:

[0096]

[0097] In S214, the event trigger function g i (t) is set as:

[0098]

[0099] wherein η∈(0,1) is a constant parameter.

[0100] According to the present application, when g i (t)≥0, the event is triggered, and the aircraft M i The state is updated at the event time.

[0101] The cooperative guidance law u ri in the direction of the line of sight is expressed as:

[0102]

[0103] wherein, represents the external disturbance of the system.

[0104] In S2, the design of the cooperative guidance law in the direction of the line of sight includes the following sub-steps:

[0105] S221, set the guidance model in the direction of the line of sight normal;

[0106] S222, set the fixed-time convergent non-singular terminal sliding mode variable with the guidance goal that all aircrafts can intercept the target at different angles;

[0107] S223, based on the guidance model and the sliding mode variable, obtain the cooperative guidance law in the direction of the line of sight normal.

[0108] In S221, the guidance model is a guidance model with reach angle constraint.

[0109] According to the present application, for each specified line of sight angle, there is a corresponding terminal reach angle, and by setting the guidance model with reach angle constraint, the aircrafts can be guaranteed to have terminal line of sight angle constraint.

[0110] The guidance model is set as:

[0111]

[0112] wherein, εqi , d qi is an intermediate variable, ε qi = q i - q di , d qi = a t cos(q i - γ t ) / r i .

[0113] In S222, all aircrafts can intercept the target at different angles as the guidance target, even if the line-of-sight angle of each aircraft converges to the desired value, and the line-of-sight angle rate converges to 0° / s.

[0114] In S222, the fixed-time convergent nonsingular terminal sliding mode variable is expressed as:

[0115]

[0116] where s i represents a sliding surface, β q1 , β q2 , α q1 , α q2 are constant parameters, preferably, β q1 , β q2 > 0, 0 < α q1 < 1, α q2 > 1, and

[0117] In S223, the cooperative guidance law u qi of the line-of-sight normal channel is expressed as:

[0118]

[0119] where c q1 , c q2 , μ q1 , μ q2 are settable parameters.

[0120] In S3, according to the present application, the external disturbance of the system is unknown and cannot be directly obtained, and traditionally, there are two methods to deal with the disturbance of the system: one is to use a sign function to suppress the overall disturbance of the system, and the other is to design an observer to approximate the disturbance of the system. Since the former puts strict requirements on the setting of the switching function and is easy to cause chattering, the present application uses a nonlinear disturbance observer with fixed-time convergence to estimate.

[0121] According to the present application, for the external disturbance of the system, the disturbance observer is used for estimation:

[0122]

[0123] Where z1 represents the first-order variable of the observer, z2 represents the second-order variable of the observer, k1, k2, k3, q, and p are configurable parameters, and ν represents a configurable parameter.

[0124] Example

[0125] Example 1

[0126] A simulation experiment was conducted in which four aircraft were set up to attack a target. The aircraft guidance law was obtained by the following steps:

[0127] S1. Establish a relative kinematic model between multiple aircraft and maneuvering targets;

[0128] S2. Based on the kinematic model, a cooperative guidance law is designed in both the line of sight tangential and line of sight normal channels to ensure consistent convergence of state variables within a fixed time.

[0129] S3. Setting up a disturbance observer to estimate and compensate for system disturbances in the cooperative guidance law;

[0130] In S1, the relative kinematic model of the multiple aircraft and the maneuvering target is expressed as:

[0131]

[0132] By taking the derivative of the first two equations of the relative kinematic model, we can obtain the acceleration components in the tangential and normal directions of the line of sight, which can be expressed as:

[0133]

[0134] in,

[0135] u ri =a vi cos(q i -γ mi )+a mi sin(q i -γ mi )

[0136] u qi =-a vi sin(q i -γ mi )+a mi cos(q i -γ mi )

[0137] In S2, the design of the collaborative guidance law for the line-of-sight tangential channel includes the following sub-steps:

[0138] S211, set multi-aircraft constraints to achieve multi-aircraft cooperative arrival to the target;

[0139] S212, set control protocol to achieve fixed time consistency of arrival time based on event-triggered mechanism;

[0140] S213, add measurement error in the control protocol;

[0141] S214, set event-triggered function based on multi-aircraft constraints and control protocol to obtain cooperative guidance law in the line-of-sight tangent direction.

[0142] In S211, the multi-aircraft constraints are expressed as:

[0143]

[0144] In S212, the control protocol is set as:

[0145]

[0146] In S213, the measurement error e i (t) is:

[0147]

[0148] The control protocol with measurement error can be expressed as:

[0149]

[0150] In S214, the event-triggered function g i (t) is set as:

[0151]

[0152] The cooperative guidance law u ri in the line-of-sight tangent direction is expressed as:

[0153]

[0154] In S2, the design of cooperative guidance law in the line-of-sight normal direction includes the following sub-steps:

[0155] S221, set the guidance model in the line-of-sight normal direction;

[0156] S222, set fixed time convergence nonsingular terminal sliding mode variables with the guidance goal that all aircraft can intercept the target at different angles;

[0157] S223, obtain cooperative guidance law in the line-of-sight normal direction based on the guidance model and sliding mode variables.

[0158] In S221, the guidance model is set as:

[0159]

[0160] ε qi = q i -q di

[0161] d qi = a t cos(q i - γ t ) / r i

[0162] In S222, the fixed-time convergent non-singular terminal sliding mode variable is expressed as:

[0163]

[0164] In S223, the cooperative guidance law u qi of the line-of-sight normal channel is expressed as:

[0165]

[0166] In S3, for the external disturbance of the system, the following disturbance observer is used:

[0167]

[0168] wherein c1=0.1, c2=0.1, c3=1, η=0.6, α=2;

[0169] β q1 =1, α q1 =0.9, β q2 =1, α q2 =2, c q1 =300, c q2 =300, μ q1 =0.4,

[0170] μ q2 =2;

[0171] k1=1, k2=2, k3=1, q=0.8, p=1.2.

[0172] In the simulation process, the target is initially located at (10000, 2000) m, and makes a constant maneuver, the target speed V t is 60 m / s, the initial trajectory angle of the target γ t is 30°, and the target maneuver size a tThe effective g-load limits of the aircraft along the tangential and normal directions of the line of sight are set to [-5g, 8g] and [-8g, 8g] respectively. The initial conditions are shown in Table 1.

[0173] Table 1

[0174] Aircraft Position / m Velocity / m / s Trajectory angle / ° Desired terminal line of sight angle q di / °]] 1 (3000,4000) 270 15 -5 2 (5000,6000) 280 -15 -25 3 (7000,8000) 290 -60 -80 4 (13000,9000) 300 -75 -110

[0175] The simulation results are as follows Figures 2-7 As shown, Figure 2 The observer error is shown in the figure. Figure 3 shows the trajectory of the aircraft in the horizontal plane. Figure 4 Shows the remaining flight time of the aircraft. Figure 5 shows the aircraft's sight angle, Figure 6 shows the aircraft-target line-of-sight angular rate, Figure 7 Aircraft overload commands are shown.

[0176] from Figure 2 It can be seen from the figure that the interference observer can accurately approximate the system interference in the line of sight tangent direction and line of sight normal direction; Figure 3 It can be seen from the figure that all four aircraft can accurately hit the target in the desired terminal line of sight direction; Figure 4 It can be seen from the figure that the remaining flight time of the four aircraft can reach consistent convergence within 5s, which shows the fast convergence characteristic of the proposed guidance law. Figure 5 It can be seen from the figure that the line of sight angle error of each aircraft can converge to 0°, which verifies the effectiveness of the line of sight normal guidance law. Figure 6 It can be seen from the figure that the line of sight angular rates of the four aircraft can gradually decrease and approach 0° / s, which can ensure that multiple aircraft can accurately hit the target. Figure 7 It can be seen that the overload instruction in the tangential direction of the line of sight is between [-5g, 8g], which can meet the available overload constraint of the aircraft; while the overload instruction in the normal direction of the line of sight is relatively large at the initial moment. This is because the relative line of sight angle deviation and line of sight angular rate are relatively large at the initial moment, but it is still maintained between [-8g, 8g], which can meet the normal overload limit requirement of the aircraft.

[0177] The present invention has been described above with reference to preferred embodiments, but these embodiments are merely exemplary and serve only as illustrations. On this basis, various replacements and improvements can be made to the present invention, all of which fall within the scope of protection of the present invention.

Claims

1. A triggered multi-aircraft cooperative guidance algorithm for maneuvering targets, characterized by: The following steps are involved: S1. Establish a relative kinematic model between multiple aircraft and maneuvering targets; S2. Based on the kinematic model, a cooperative guidance law is designed in both the line of sight tangential and line of sight normal channels to ensure consistent convergence of state variables within a fixed time. S3. Setting up a disturbance observer to estimate and compensate for system disturbances in the cooperative guidance law; S4. The aircraft flies using the cooperative guidance law after compensating for system disturbances.

2. The trigger-type multi-aircraft cooperative guidance algorithm for maneuvering targets according to claim 1 is characterized in that: The relative kinematic model of the multi-aircraft and the maneuvering target is expressed as: Among them, r i Indicates aircraft M i The distance from the target T, V mi Indicates aircraft M i Speed, V t represents the speed of the target, q i Indicates aircraft M i The viewing angle, γ mi Indicates aircraft M i The ballistic deflection angle, γ t Indicates the target's trajectory angle, a mi Indicates aircraft M i The normal acceleration, a t represents the normal acceleration of the target, a vi Indicates aircraft M i The tangential acceleration of Based on the relative kinematics model, the acceleration components of the tangential and normal directions of the line of sight are obtained, which are expressed as: Among them, u ri is the acceleration component tangential to the line of sight, u qi is the acceleration component in the normal direction of the line of sight, expressed as: you ri =a vi cos(q i -c mi )+a mi sin(q i -c mi ) you qi =-a vi sin(q i -c mi )+a mi cos(q i -c mi )。 3. The trigger-type multi-aircraft cooperative guidance algorithm for maneuvering targets according to claim 1 is characterized in that: In S2, the design of the collaborative guidance law for the line-of-sight tangential channel includes the following sub-steps: S211. Setting multi-aircraft restrictions to achieve coordinated arrival of multiple aircraft at the target; S212. Setting a control protocol to achieve fixed time consistency of arrival time based on an event trigger mechanism; S213, adding measurement error to the control protocol; S214: Set an event trigger function to obtain a coordinated guidance law in the line of sight tangent direction based on multi-aircraft restrictions and control protocols.

4. The trigger-type multi-aircraft cooperative guidance algorithm for maneuvering targets according to claim 3 is characterized in that: In S211, the multi-aircraft restriction is expressed as: Among them, t goi Indicates aircraft M i The remaining flight time, t goj Indicates aircraft M j The remaining flight time, t fi Indicates aircraft M i The total flight time, q di Indicates aircraft M i The expected sight angle.

5. The triggered multi-aircraft cooperative guidance algorithm for maneuvering targets according to claim 3 is characterized in that: The control protocol with measurement error is expressed as: Among them, e i (t) is the measurement error, set as: in, Indicates aircraft M i The control protocol is: c1, c2, c3 are control gain parameters, α is a constant parameter greater than 1, Indicates aircraft M i The most recent event triggering time k.

6. The triggered multi-aircraft cooperative guidance algorithm for maneuvering targets according to claim 3 is characterized in that: In S214, the event triggers function g i (t) is set to: Among them, η∈(0,1) is a constant parameter.

7. The triggered multi-aircraft cooperative guidance algorithm for maneuvering targets according to claim 6 is characterized in that: The coordinated guidance law u in the tangential direction of the line of sight ri Expressed as: in, Indicates external interference to the system.

8. The trigger-type multi-aircraft cooperative guidance algorithm for maneuvering targets according to claim 1 is characterized in that: In S2, the design of the collaborative guidance law for the line-of-sight normal channel includes the following sub-steps: S221. Setting the guidance model in the normal direction of the sight line; S222, taking the guidance goal of all aircraft being able to intercept the target at different angles, setting a fixed-time convergence non-singular terminal sliding mode variable; S223. Based on the guidance model and sliding mode variables, a collaborative guidance law for the line-of-sight normal channel is obtained.

9. The triggered multi-aircraft cooperative guidance algorithm for maneuvering targets according to claim 8, characterized in that: In S221, the guidance model is set to: Among them, ε qi d qi is the intermediate variable, ε qi =q i -q di , d qi =a t cos(q i -γ t ) / r i .

10. The triggered multi-aircraft cooperative guidance algorithm for maneuvering targets according to claim 8, characterized in that: In S222, the fixed-time convergent non-singular terminal sliding mode variable is expressed as: Among them, s i represents the sliding surface, β q1 , β q2 , α q1 , α q2 is a constant parameter.

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