Cooperative guidance method for multi-group aircrafts to time-sharing attack on multiple targets

Abstract

This invention designs a cooperative guidance method for time-sharing attacks on multiple targets by multiple groups of aircraft. This method enables aircraft belonging to different groups within a swarm to sequentially hit different targets at specified attack times and time intervals. Specifically, it includes: Step 1: Constructing the communication topology of the multi-group interconnected network; Step 2: Establishing a motion relationship model between the multiple groups of aircraft and the target; Step 3: Predicting the remaining hit time of the aircraft; Step 4: Defining the error variable for time-consistent distributed multi-group coordinated time-sharing attacks on multiple targets; Step 5: Introducing a time-varying function; Step 6: Giving the distributed coordinated guidance law for time-sharing attacks on multiple targets by multiple groups of aircraft with attack time control. Compared with existing cooperative guidance methods, the designed method enables aircraft from different groups within a multi-group swarm to sequentially hit different targets at specified attack times and time intervals.

Description

Technical Field

[0001] This invention relates to a collaborative guidance method for multi-target time-sharing strikes by multiple groups of aircraft, belonging to the field of aircraft guidance and control. Specifically, it is an invention of a distributed collaborative guidance method for multi-target time-sharing strikes by multiple groups of aircraft with attack time control and fixed-time convergence, which enables multiple groups of aircraft that can communicate with each other to sequentially and collaboratively hit different targets at specified attack times and attack time intervals, and ensures that the distributed multi-group multi-target collaborative time-sharing strike error can converge within a fixed time. Background Technology

[0002] Cooperative guidance methods enable aircraft to simultaneously hit targets, offering unique advantages for missions requiring coordinated attacks. Existing cooperative guidance methods primarily control coordinated attacks by constructing and stably converging cooperative errors. However, these methods only guarantee that each aircraft in a group can simultaneously hit a single target, failing to meet the requirement of multiple groups of aircraft capable of communication coordinating to sequentially and cooperatively hit different targets at specified attack times and intervals. Attack time convergence methods primarily include asymptotic time convergence and finite time convergence. Asymptotic time convergence guarantees zero attack time error, but the convergence time tends towards infinity. For attack time control guidance methods, the attack time error should converge before the desired attack time. If the algorithm's convergence time exceeds the expected attack time, the final attack time will differ from the expected attack time. While finite time control methods guarantee error convergence within a finite time, the upper bound of the convergence time depends on the initial system state. For systems where the initial state is difficult to measure, the upper bound of the convergence time cannot be predicted. In light of this, researchers have proposed a fixed-time convergence method that does not depend on the initial state values ​​of the system.

[0003] Therefore, this invention designs a multi-group aircraft time-sharing coordinated guidance method for multi-target attack based on fixed-time convergence theory. The constructed distributed multi-group multi-target coordinated time-sharing attack error enables the aircraft swarm to sequentially hit different targets at specified attack times and time intervals. The fixed-time convergence method allows the coordinated time-sharing attack error to converge rapidly before the first aircraft hits the target. The designed method enables multiple groups of aircraft to sequentially hit different targets at specified attack times and time intervals. Summary of the Invention

[0004] This invention addresses the problem of multiple groups of aircraft sequentially hitting different targets at specified attack times and time intervals. It proposes a time-sharing cooperative guidance method for multi-target strikes by multiple groups of aircraft, based on fixed-time convergence theory. This method enables rapid convergence of errors in the constructed distributed multi-group multi-target cooperative time-sharing strike, thus achieving time-sharing strikes by multiple groups against multiple targets.

[0005] The technical concept of this invention is to design a time-sharing cooperative strike guidance law with fixed-time convergence for multiple groups of aircraft, enabling these groups to sequentially hit different targets at specified time intervals. This method first establishes a mathematical model of the motion of multiple groups of aircraft relative to the target, where communication is possible not only between aircraft within a group but also between aircraft belonging to different groups. It further predicts the remaining hit time for the multiple groups of aircraft and constructs a distributed multi-group, multi-target cooperative time-sharing strike error. Finally, it guarantees a time-sharing cooperative strike guidance law that ensures the fixed-time convergence of the distributed multi-group cooperative time-sharing strike error.

[0006] This invention relates to a cooperative guidance method for time-sharing strikes against multiple targets by multiple groups of aircraft, comprising the following steps:

[0007] Step 1: Construct the communication topology of the multi-group interconnected network.

[0008] If a multi-group aircraft cluster contains n aircraft, and these n aircraft belong to α groups that can communicate with each other, then the relationship between the aircraft and the groups can be defined as: the nth... m-1 +1 to the nth m The aircraft belongs to the m-th group, where 0 ≤ n. m-1 ≤n m ≤n,1≤m≤α,n m-1 ,n m n, m and α are all positive integers.

[0009] Step 2: Establish a motion relationship model between the aircraft and the target.

[0010] If the i-th aircraft belongs to the m-th group, then define and Let x, y, and z represent the position and velocity vectors of the aircraft in the inertial coordinate system, respectively. The motion of the aircraft in three-dimensional space can be represented as:

[0011]

[0012] In the formula, V i m , and Let these represent the aircraft's velocity, track inclination angle, and track deflection angle, respectively. Their dynamic equations satisfy:

[0013]

[0014] In the formula, and These represent the acceleration components in the x, y, and z directions in the ballistic coordinate system, respectively.

[0015] Define acceleration components in the inertial coordinate system and for:

[0016]

[0017] Inertial coordinate system acceleration components and acceleration components in the ballistic coordinate system and The conversion relationship is as follows:

[0018]

[0019] If the i-th aircraft belongs to the m-th group, then its relative motion relationship with the k-th target in the line-of-sight coordinate system can be expressed as:

[0020]

[0021] In the formula, Let be the distance between the i-th aircraft in the m-th group and the k-th target. and Indicates the angle of inclination and the angle of deflection of the line of sight. This represents the acceleration vector in the line-of-sight coordinates.

[0022] The transformation relationship of the acceleration vector from the inertial coordinate system to the line-of-sight coordinate system is as follows:

[0023]

[0024] The following formula can be used to calculate the position information of the aircraft and the target. and information:

[0025]

[0026]

[0027]

[0028] In the formula, This represents the position coordinates of the k-th target in the inertial coordinate system.

[0029] Step 3: Predict the remaining hit time for each aircraft.

[0030] If the i-th aircraft belongs to the m-th group, then its remaining hit time against the k-th target is... The following formula can be used for prediction:

[0031]

[0032] Step 4: Define the error variable for time-consistent distributed multi-group multi-target collaborative time-sharing attack.

[0033] The time-sharing strike coordination error variable between the various aircraft is defined as follows:

[0034]

[0035] In the formula, a ij It is the element corresponding to the i-th row and j-th column of the adjacency matrix of the communication topology graph. If the i-th aircraft can receive the information from the j-th aircraft, a ij =1, otherwise a ij =0. τ m Let β represent the specified attack time interval for the m-th group. If both the j-th and i-th aircraft belong to the m-th group, then β = m; otherwise, β ≠ m, where 1 ≤ β ≤ α and β is a positive integer. If τ m >τ β Then, after all the aircraft in the m-th group have jointly hit the target to be attacked by the aircraft in the β-th group, they simultaneously hit the target to be attacked by the m-th group, and the time interval between the m-th group and the β-th group hitting their respective targets is τ. m -τ β μ i Indicates whether the i-th aircraft can receive the attack time command T. d If it can be received, then μ i =1, otherwise μ i =0. Using the formula above, the time when each aircraft in the m-th group hits the k-th target can be T. d +τ m .

[0036] Step 5: Introduce a time-varying function.

[0037] For guidance law design purposes, a time-varying function is introduced:

[0038]

[0039] In the formula, h≥2 is a positive real number, and T f >0.

[0040] The first-order time derivative of Ψ satisfies:

[0041]

[0042] Step 6: Propose the cooperative guidance law for multi-vehicle time-sharing strikes.

[0043] The guidance law design for multi-vehicle coordinated time-sharing strike is as follows:

[0044]

[0045] In the formula, k1, k2 > 0, 0 < α1 < 1, β1 > 1, and k3 and k4 are positive real numbers.

[0046] The beneficial effects of this invention are as follows: a cooperative guidance method for multi-group aircraft to attack multiple targets in a time-sharing manner is designed, so that aircraft belonging to different groups in a multi-group aircraft cluster can hit different targets sequentially at specified attack times and attack time intervals. Attached Figure Description

[0047] Figure 1 This is a communication topology diagram between aircraft in a simulation embodiment.

[0048] Figure 2 It is the trajectory curve of a spacecraft under the distributed attack time control multi-group spacecraft's time-sharing coordinated guidance law for attacking multiple targets.

[0049] Figure 3 It is the distance change curve between the aircraft and the target under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target strikes.

[0050] Figure 4 It is the curve of the cooperative error variation of the aircraft in group 1 under the distributed attack time control multi-group aircraft cooperative guidance law for multi-target time-sharing attack.

[0051] Figure 5 It is the curve of the cooperative error variation of the aircraft in group 2 under the distributed attack time control multi-group aircraft cooperative guidance law for multi-target time-sharing attack.

[0052] Figure 6 It is the curve of the cooperative error variation of the aircraft in group 3 under the distributed attack time control multi-group aircraft cooperative guidance law for multi-target time-sharing attack.

[0053] Figure 7 It is the curve of the line-of-sight tilt angle and angular rate change of the aircraft in group 1 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack.

[0054] Figure 8 It is the curve of the line-of-sight tilt angle and angular rate change of the aircraft in group 2 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack.

[0055] Figure 9 It is the curve of the line-of-sight tilt angle and angular rate change of the aircraft in group 3 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack.

[0056] Figure 10It is the curve of the line-of-sight deflection angle and angular rate change of the aircraft in group 1 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack.

[0057] Figure 11 It is the curve of the line-of-sight deflection angle and angular rate change of the aircraft in group 2 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack.

[0058] Figure 12 It is the curve of the line-of-sight deflection angle and angular rate change of the aircraft in group 3 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack.

[0059] Figure 13 It is the curve of the line-of-sight acceleration change of the aircraft in group 1 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack.

[0060] Figure 14 It is the curve of the line-of-sight acceleration change of the aircraft in group 2 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack.

[0061] Figure 15 It is the curve of the line-of-sight acceleration change of the aircraft in group 3 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack.

[0062] Figure 16 It is the acceleration change curve of the line-of-sight tilt angle direction of the aircraft in group 1 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target strikes.

[0063] Figure 17 It is the curve of the acceleration change in the line-of-sight tilt direction of the aircraft in group 2 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target strikes.

[0064] Figure 18 It is the acceleration change curve of the line-of-sight tilt angle of the aircraft in group 3 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack.

[0065] Figure 19 It is the acceleration change curve of the line-of-sight deflection direction of the aircraft in group 1 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack.

[0066] Figure 20 It is the acceleration change curve of the line-of-sight deflection direction of the aircraft in group 2 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target strikes.

[0067] Figure 21It is the acceleration change curve of the line-of-sight deflection direction of the aircraft in group 3 under the distributed attack time control multi-group aircraft's time-sharing coordinated guidance law for multi-target attack. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of this invention clearer, please refer to the appendix. Figure 1 —21. Further explanation of the present invention.

[0069] This invention discloses a cooperative guidance method for multi-target time-sharing strikes by multiple groups of aircraft, comprising the following steps:

[0070] Step 1: Construct the communication topology of the multi-group interconnected network.

[0071] If a multi-group aircraft cluster contains n aircraft, and these n aircraft belong to α groups that can communicate with each other, then the relationship between the aircraft and the groups can be defined as: the nth... m-1 +1 to the nth m The aircraft belongs to the m-th group, where 0 ≤ n. m-1 ≤n m ≤n,1≤m≤α,n m-1 ,n m n, m and α are all positive integers.

[0072] Step 2: Establish a motion relationship model between the aircraft and the target.

[0073] If the i-th aircraft belongs to the m-th group, then define and Let x, y, and z represent the position and velocity vectors of the aircraft in the inertial coordinate system, respectively. The motion of the aircraft in three-dimensional space can be represented as:

[0074]

[0075] In the formula, V i m , and Let these represent the aircraft's velocity, track inclination angle, and track deflection angle, respectively. Their dynamic equations satisfy:

[0076]

[0077] In the formula, and These represent the acceleration components in the x, y, and z directions in the ballistic coordinate system, respectively.

[0078] Define acceleration components in the inertial coordinate system and for:

[0079]

[0080] Inertial coordinate system acceleration components and acceleration components in the ballistic coordinate system and The conversion relationship is as follows:

[0081]

[0082] If the i-th aircraft belongs to the m-th group, then its relative motion relationship with the k-th target in the line-of-sight coordinate system can be expressed as:

[0083]

[0084] In the formula, Let be the distance between the i-th aircraft in the m-th group and the k-th target. and Indicates the angle of inclination and the angle of deflection of the line of sight. This represents the acceleration vector in the line-of-sight coordinates.

[0085] The transformation relationship of the acceleration vector from the inertial coordinate system to the line-of-sight coordinate system is as follows:

[0086]

[0087] The following formula can be used to calculate the position information of the aircraft and the target. and information:

[0088]

[0089]

[0090]

[0091] In the formula, This represents the position coordinates of the k-th target in the inertial coordinate system.

[0092] Step 3: Predict the remaining hit time for each aircraft.

[0093] If the i-th aircraft belongs to the m-th group, then its remaining hit time against the k-th target is... The following formula can be used for prediction:

[0094]

[0095] Step 4: Define the error variable for time-consistent distributed multi-group multi-target collaborative time-sharing attack.

[0096] The time-sharing strike coordination error variable between the various aircraft is defined as follows:

[0097]

[0098] In the formula a ij It is the element corresponding to the i-th row and j-th column of the adjacency matrix of the communication topology graph. If the i-th aircraft can receive the information from the j-th aircraft, a ij =1, otherwise a ij =0. τ m Let β represent the specified attack time interval for the m-th group. If both the j-th and i-th aircraft belong to the m-th group, then β = m; otherwise, β ≠ m, where 1 ≤ β ≤ α and β is a positive integer. If τ m >τ β Then, after all the aircraft in the m-th group have jointly hit the target to be attacked by the aircraft in the β-th group, they simultaneously hit the target to be attacked by the m-th group, and the time interval between the m-th group and the β-th group hitting their respective targets is τ. m -τ β μ i Indicates whether the i-th aircraft can receive the attack time command T. d If it can be received, then μ i =1, otherwise μ i =0. Using the formula above, the time when each aircraft in the m-th group hits the k-th target can be T. d +τ m .

[0099] Step 5: Introduce a time-varying function.

[0100] For guidance law design purposes, a time-varying function is introduced:

[0101]

[0102] In the formula, h≥2 is a positive real number, and T f >0.

[0103] The first-order time derivative of Ψ satisfies:

[0104]

[0105] Step 6: Propose the cooperative guidance law for multi-vehicle time-sharing strikes.

[0106] The guidance law design for multi-vehicle coordinated time-sharing strike is as follows:

[0107]

[0108] In the formula, k1, k2 > 0, 0 < α1 < 1, β1 > 1, and k3 and k4 are positive real numbers.

[0109] The designed algorithm was verified using the Matlab simulation platform to validate the effectiveness of the distributed, time-sharing coordinated guidance method for multi-target strikes by multiple groups of aircraft with attack time control. For the example, a scenario was set where a cluster of three aircraft attacked three stationary targets. The parameters were set as follows: k1 = 3, k2 = 3, α1 = 0.9, β1 = 2, k3 = 20, k4 = 20, T... f =20,h=3,τ1=12s,τ1=5s,τ1=0,T d =40s. Considering practical considerations, the acceleration limit is ±100m / s². 2 The initial positions of targets 1, 2, and 3 are (0,0,0), (2000,0,0), and (0,2000,0), respectively. The initial data for each aircraft is shown in Table 1. The communication topology between the aircraft is as follows: Figure 1 As shown, 1-15 represent aircraft 1-15 respectively. Aircraft 1-5 belong to group 1, aircraft 6-10 belong to group 2, and aircraft 11-15 belong to group 3. If two aircraft are connected by an arrow, it means that the two aircraft can communicate with each other to exchange and coordinate time-sharing attack errors. The aircraft represented by the orange circle can receive the attack time command T. d .

[0110] Table 1 Initial parameter settings for each aircraft

[0111]

[0112] Simulation results of coordinated guidance for multi-target time-sharing strikes by multi-group aircraft swarms are shown below. Figures 2-21 ,like Figure 2 and Figure 3 As shown, groups of aircraft in a swarm sequentially hit targets at specified attack times and intervals. Figures 4-6 It can be seen that the cooperative error converges rapidly before hitting the target. From... Figures 7-12 It can be seen that the angular velocity of the line of sight tilt and the angular velocity of the line of sight deflection are related to T. f The system converges rapidly to achieve the desired control effect.

Claims

1. A cooperative guidance method for multi-group aircraft to engage multiple targets in a time-sharing manner, characterized in that: Includes the following steps: Step 1: Construct the communication topology of the multi-group interconnected network; If a multi-group aircraft cluster has a total of n This aircraft n The aircraft belong to The relationship between an aircraft and a group that communicates with each other is defined as follows: The first The aircraft belonged to the first m There are several groups, among which... and All are positive integers; Step 2: Establish a motion model of the aircraft relative to the target; If the first i The aircraft belonged to the first m Groups, defined and These represent the aircraft in the inertial coordinate system. x , y , z The position and velocity vectors in the direction; the motion relationship of the aircraft in three-dimensional space is represented as: ； In the formula, , and These represent the aircraft's speed, track inclination angle, and track deflection angle, respectively. Step 3: Predict the remaining hit time for each aircraft; If the first i The aircraft belongs to the first m The nth group, then its relationship with the nth group k Remaining time to hit each target Prediction is made using the following formula: ； Step 4: Define the time-consistent distributed multi-group multi-target collaborative time-sharing attack error variable; The time-sharing strike coordination error variable between the various aircraft is defined as follows: ； In the formula, a ij It is the adjacency matrix of the communication topology graph. i Line number j The element corresponding to the column; Step 5: Introduce a time-varying function; For guidance law design purposes, a time-varying function is introduced: ； In the formula, h ≥2 is a positive real number. T f >0; Step 6: Propose the cooperative guidance law for multi-vehicle time-sharing strikes; The guidance law design for multi-vehicle coordinated time-sharing strike is as follows: ； In the formula, , k 3 and k 4 is a positive real number; For the first m The first group i The aircraft relative to the first k Distance to each target and Indicates the angle of inclination and the angle of deflection of the line of sight. This represents the acceleration vector in the line-of-sight coordinate system. In step 4, if the first i The aircraft is able to receive the first j Information about the aircraft a ij =1, otherwise a ij =0; Indicates the first m The specified attack time interval for each group, if the first group... j aircraft and the first i All aircraft belong to the first m If there are several groups, then ,on the contrary ,in and It is a positive integer; Among them, if Then the first m Each aircraft in the group was in the The aircraft in each group cooperated to hit the first... After the target of each group is attacked, the first one is hit simultaneously. m The target to be attacked by each group, and the first m Group 1 and the 2nd The time interval between each group hitting its respective target is ; Indicates the first i Can the aircraft receive the attack time command? If acceptable ,on the contrary ; make the first m Each aircraft in the group hit the first k The time for the target is .

2. The cooperative guidance method for multi-target time-sharing strikes by multiple groups of aircraft according to claim 1, characterized in that: In step 2, the dynamic equations for the aircraft velocity, track inclination angle, and track deflection angle satisfy: ； In the formula, , and Representing the ballistic coordinates respectively x , y and z The acceleration component in the direction.

3. The cooperative guidance method for multi-target time-sharing strikes by multiple groups of aircraft according to claim 2, characterized in that: Define acceleration components in the inertial coordinate system , and for: 。 4. The cooperative guidance method for multi-target time-sharing strikes by multiple groups of aircraft according to claim 2 or 3, characterized in that: Inertial coordinate system acceleration components , and acceleration components in the ballistic coordinate system , and The conversion relationship is as follows: 。 5. The cooperative guidance method for multi-target time-sharing strikes by multiple groups of aircraft according to claim 4, characterized in that: In step 2, if the first i The aircraft belonged to the first m The nth group, then its position in the line-of-sight coordinate system is the nth group. k The relative motion relationships of the targets are expressed as follows: ； In the formula, For the first m The first group i The aircraft relative to the first k Distance to each target and Indicates the angle of inclination and the angle of deflection of the line of sight. This represents the acceleration vector in the line-of-sight coordinates.

6. The cooperative guidance method for multi-target time-sharing strikes by multiple groups of aircraft according to claim 5, characterized in that: The transformation relationship of the acceleration vector from the inertial coordinate system to the line-of-sight coordinate system is as follows: 。 7. The cooperative guidance method for multi-target time-sharing strikes by multiple groups of aircraft according to claim 5, characterized in that: In step 2, the following formula is used to calculate the position information of the aircraft and the target. , and information: ； ； ； In the formula, Indicates the first k The position coordinates of the target in the inertial coordinate system.

8. The cooperative guidance method for multi-target time-sharing strikes by multiple groups of aircraft according to claim 1, characterized in that: In step 5, Ψ The first-order time derivative satisfies: 。

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