Three-Dimensional Event-Triggered Cooperative Guidance Method

Abstract

The present invention provides a three-dimensional event-triggered cooperative guidance method, comprising the following steps: constructing a cooperative guidance command in a first direction and a first trigger mechanism, and updating the cooperative guidance command in the first direction according to the first trigger mechanism; constructing a cooperative guidance command in a second direction and a second trigger mechanism, and updating the cooperative guidance command in the second direction according to the second trigger mechanism; constructing a cooperative guidance command in a third direction and a third trigger mechanism, and updating the cooperative guidance command in the third direction according to the third trigger mechanism; the cooperative guidance commands in the first and second directions control multiple missiles to attack at a desired relative collision angle, the cooperative guidance command in the third direction controls multiple missiles to achieve simultaneous attack, any two of the first, second, and third directions are perpendicular to each other, and at least one of the first, second, and third trigger mechanisms is event-triggered. By applying the technical solution of the present invention, the update frequency of the guidance command can be greatly reduced, thereby reducing resource consumption.

Description

Technical Field

[0001] The present invention relates to the field of aircraft control, and more particularly, to a three-dimensional event-triggered cooperative guidance method. Background Art

[0002] Recently, due to the increasingly perfect multi-layer defense system of missiles and the enhanced maneuverability of targets, it has become more and more difficult to penetrate targets using traditional single missiles. In this context, the concept of cooperative guidance has been proposed as an effective countermeasure to enhance the penetration ability of missiles. In addition to achieving a small or even zero miss distance, the cooperative guidance law is also required to satisfy the constraints in the time and space dimensions to improve the lethality of multiple missiles.

[0003] Time cooperative guidance means that multiple missiles attack a target simultaneously, which can be achieved in two ways. The first method is called impact time control guidance (ITCG), which requires all missiles to attack the target at a pre-specified common impact time. However, it is difficult to allocate a suitable common impact time in advance for multiple missiles in different initial conditions. In the second method, multiple missiles coordinate their launch times to reach an agreement to achieve simultaneous attack through the communication topology. At this time, an explicit expression of time estimation is used for time cooperative guidance. However, due to the large initial heading error, it is challenging to accurately estimate the remaining time, and unknown target maneuvers and external disturbances will reduce the performance of cooperative guidance.

[0004] Space cooperative guidance means that multiple missiles attack a target at different impact angles to improve lethality. A conventional cooperative guidance law with impact angle constraints is achieved by specifying the required impact angle for each missile before engagement. Therefore, under uncertain conditions such as unknown target maneuvers and disturbances, multiple missiles may frequently adjust the guidance commands to reach and maintain the required impact angles. Therefore, the guidance law with a specific desired collision angle may lead to unnecessary fuel consumption.

[0005] More importantly, the multi-missile system is a network framework that requires limited resources, such as maneuvering energy, computing power, and processor memory. Existing cooperative guidance laws require the cooperative guidance commands to be continuously updated with input signals sent periodically, called time-triggered guidance. Even if the coordinated variables do not change significantly, the high update frequency of the guidance commands will waste computing resources. Therefore, time-triggered guidance may require a heavy computing burden and transmission load in the controller-to-actuator channel. Summary of the Invention

[0006] The main object of the present invention is to provide a three-dimensional event-triggered cooperative guidance method to solve the technical problem of resource waste caused by frequent update of guidance commands in the prior art.

[0007] The present invention provides a three-dimensional event-triggered cooperative guidance method, including the following steps: constructing a cooperative guidance command in a first direction and a first trigger mechanism, and updating the cooperative guidance command in the first direction according to the first trigger mechanism; constructing a cooperative guidance command in a second direction and a second trigger mechanism, and updating the cooperative guidance command in the second direction according to the second trigger mechanism; constructing a cooperative guidance command in a third direction and a third trigger mechanism, and updating the cooperative guidance command in the third direction according to the third trigger mechanism; the cooperative guidance commands in the first direction and the second direction control multiple missiles to attack at a desired relative collision angle, and the cooperative guidance command in the third direction controls multiple missiles to achieve simultaneous attack, any two of the first direction, the second direction, and the third direction are perpendicular to each other, and at least one of the first trigger mechanism, the second trigger mechanism, and the third trigger mechanism is event-triggered.

[0008] Further, the first direction is along the line-of-sight elevation direction, the second direction is along the line-of-sight azimuth direction, and the third direction is along the line-of-sight direction.

[0009] Further, constructing the cooperative guidance command in the first direction specifically includes: constructing the consistency error of the relative line-of-sight angle in the first direction; constructing the consistency error of the angular rate in the first direction; constructing the tracking error of the angular rate in the first direction according to the consistency error of the relative line-of-sight angle in the first direction; constructing the cooperative guidance command in the first direction according to the consistency error of the relative line-of-sight angle in the first direction, the consistency error of the angular rate in the first direction, and the tracking error of the angular rate in the first direction.

[0010] Further, constructing the cooperative guidance command in the second direction specifically includes: constructing the consistency error of the relative line-of-sight angle in the second direction; constructing the consistency error of the angular rate in the second direction; constructing the tracking error of the angular rate in the second direction according to the consistency error of the relative line-of-sight angle in the second direction; constructing the cooperative guidance command in the second direction according to the consistency error of the relative line-of-sight angle in the second direction, the consistency error of the angular rate in the second direction, and the tracking error of the angular rate in the second direction.

[0011] Further, constructing the cooperative guidance command in the third direction specifically includes: constructing the consistency error of the remaining flight distance; constructing the consistency error of the radial relative velocity; designing the cooperative guidance command in the third direction according to the consistency error of the remaining flight distance and the consistency error of the radial relative velocity.

[0012] Further, the cooperative guidance command in the first direction

[0013]

[0014] where, a Mεi (t) is the guidance command of the i-th missile in the first direction, r i (t) is the relative distance between the i-th missile and the target, t is the current time, qεi (t) is the line-of-sight angle of the i-th missile in the first direction, q βi (t) is the line-of-sight angle of the i-th missile in the second direction, α ε1 、α ε2 、α ε3 、α ε4 and μ ε are all positive constants, b ε and c ε are two positive odd numbers satisfying b ε / c ε > 2, is the trigger time closest to the current time for the i-th missile, and is the next trigger time, Ξ i (t) is the consistency error of the relative line-of-sight angle of the i-th missile in the first direction. Π i (t) is the consistency error of the angular rate of the i-th missile in the first direction, e vεi (t) is the tracking error of the angular rate of the i-th missile in the first direction, p ε and g ε are two positive odd numbers satisfying p ε / g ε > 1.

[0015] Furthermore, the cooperative guidance command in the second direction

[0016]

[0017] where, a Mβi (t) is the guidance command of the i-th missile in the second direction, α β1 ,α β2 ,α β3 ,α β4 and μ β are positive constants, b β and c β are two positive odd numbers satisfying b β / c β > 2, Υ i (t) is the consistency error of the relative line-of-sight angle of the i-th missile in the second direction, Ψ i (t) is the consistency error of the angular rate of the i-th missile in the second direction, e vβi (t) is the tracking error of the angular rate of the i-th missile in the second direction, p β and g β are two positive odd numbers satisfying p β / g β > 1.

[0018] Furthermore, the cooperative guidance command in the third direction

[0019]

[0020] where a Mri (t) is the guidance command of the i-th missile along the line of sight, and α r1 , α r2 , α r3 , α r4 and μ r are all positive constants, b r and c r are two positive odd numbers satisfying b r / c r > 2, and Γ i (t) is the consistency error of the remaining flight distance of the i-th missile, and α r3 , α r4 are all positive constants, t is the current time, is the triggering moment closest to the current time for the i-th missile, and is 's next triggering moment, and Λ i (t) is the consistency error of the radial relative velocity of the i-th missile, and e vri (t) is the velocity tracking error of the i-th missile, and p r and g r are two positive odd numbers satisfying p r / g r > 1.

[0021] Furthermore, the first triggering mechanism

[0022] where

[0023]

[0024] where Θ εi (t) is the triggering error of the i-th missile in the first direction, and 0 < η ε < 1.

[0025] Furthermore, the second triggering mechanism

[0026] where

[0027]

[0028] where Θ βi (t) is the triggering error of the i-th missile in the second direction, and 0 < η β < 1.

[0029] Furthermore, the third triggering mechanism

[0030] Among them,

[0031]

[0032] Among them, Θ ri (t) is the triggering error between the most recent triggering state and the current state of the i-th missile, 0 < η r < 1.

[0033] The advantages and beneficial effects of the present invention are as follows:

[0034] Applying the three-dimensional event-triggered cooperative guidance method proposed by the technical solution of the present invention, considering the constraints in the time and space dimensions, instead of specifying a specific impact angle for each missile before launch, only the required relative collision angle is specified in advance to achieve spatial cooperative guidance. At the same time, adopting the event-triggered method, the cooperative guidance command will not be updated and remains unchanged until the triggering condition is met, which can greatly reduce the update frequency of the guidance command, thereby reducing resource consumption and ensuring good guidance performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of three-dimensional event-triggered cooperative guidance provided according to a specific embodiment of the present invention.

[0036] Figure 2 Schematic diagram of event triggering provided according to a specific embodiment of the present invention.

[0037] Figure 3 Trajectory schematic diagram of four missiles attacking a maneuvering target in the event-triggered guidance mode provided according to a specific embodiment of the present invention.

[0038] Figure 4 Comparison diagram of the triggering times of the line-of-sight direction guidance ratio provided according to a specific embodiment of the present invention.

[0039] Figure 5 Comparison diagram of the triggering times of the line-of-sight elevation direction guidance ratio provided according to a specific embodiment of the present invention.

[0040] Figure 6 Comparison diagram of the triggering times of the line-of-sight azimuth direction guidance ratio provided according to a specific embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments may be combined with each other. The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and in no way constitutes a limitation to the present invention and its application or use. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without creative efforts fall within the scope of protection of the present invention.

[0042] Step S1, construct a collaborative guidance command in the first direction and a first trigger mechanism, and update the collaborative guidance command in the first direction according to the first trigger mechanism, specifically including:

[0043] Step S101, construct the consistency error of the relative line-of-sight angle in the first direction.

[0044] Step S102, construct the consistency error of the angular rate in the first direction;

[0045] Step S103, construct the tracking error of the angular rate in the first direction according to the consistency error of the relative line-of-sight angle in the first direction;

[0046] Step S104, construct the collaborative guidance command in the first direction according to the consistency error of the relative line-of-sight angle in the first direction, the consistency error of the angular rate in the first direction, and the tracking error of the angular rate in the first direction

[0047]

[0048] where a Mεi (t) is the guidance command of the i-th missile in the first direction, r i (t) is the relative distance between the i-th missile and the target, t is the current time, q εi (t) is the line-of-sight angle of the i-th missile in the first direction, q βi (t) is the line-of-sight angle of the i-th missile in the second direction, α ε1 、α ε2 、α ε3 、α ε4 and μ ε are all positive constants, b ε and c ε are two positive odd numbers satisfying b ε / c ε > 2, is the trigger moment closest to the current time of the i-th missile, and is the next trigger moment, Ξi $(t)$ is the consistency error of the relative line-of-sight angle of the $i$-th missile in the first direction. $\Pi$ i $(t)$ is the consistency error of the angular rate of the $i$-th missile in the first direction, $e$ vεi $(t)$ is the tracking error of the angular rate of the $i$-th missile in the first direction, $p$ ε and $g$ ε are two positive odd numbers satisfying $p$ ε / $g$ ε > 1.

[0049] Construct a first trigger mechanism, and update the cooperative guidance command in the first direction according to the first trigger mechanism,

[0050] wherein,

[0051]

[0052] wherein, $\Theta$ εi $(t)$ is the trigger error of the $i$-th missile in the first direction, $0 < \eta$ ε < 1.

[0053] According to a specific embodiment of the present invention, the first direction is along the line-of-sight vertical direction, the consistency error of the relative line-of-sight angle along the line-of-sight vertical direction the consistency error of the angular rate along the line-of-sight vertical direction the tracking error of the angular rate along the line-of-sight vertical direction wherein, $\Xi$ i (t) is the consistency error of the relative line-of-sight angle of the $i$-th missile along the line-of-sight vertical direction, $i$ is a positive integer, $j$ is a positive integer, $i \in [1, N]$, $j \in [1, N]$, $N$ is the total number of missiles, when the missiles can detect each other $a$ ij = 1, otherwise $a$ ij = 0, $t$ is the current time, is the line-of-sight angle of the $i$-th missile along the line-of-sight vertical direction and the expected line-of-sight angle of the $i$-th missile along the line-of-sight vertical direction, is the line-of-sight angle of the $j$-th missile in the vertical direction and the expected line-of-sight angle of the $j$-th missile in the vertical direction, $\Pi$ i (t) is the consistency error of the angular rate of the $i$-th missile along the line-of-sight vertical direction, $q$ εi (t) is the line-of-sight angle of the $i$-th missile along the line-of-sight vertical direction, $q$ εj (t) is the line-of-sight angle of the $j$-th missile along the line-of-sight vertical direction, $e$ vεi (t) is the tracking error of the angular rate of the $i$-th missile along the line-of-sight vertical direction, $\alpha$ ε1 、$\alpha$ ε2 and $\mu$ ε are all positive constants, $b$ ε and $c$ εare two positive odd numbers that satisfy b ε / c ε > 2.

[0054] Applying this configuration method, by constructing a cooperative guidance command along the line-of-sight height direction, and only using the consistent error of the relative line-of-sight angle along the line-of-sight height direction as the coordination variable to achieve spatial cooperative guidance along the line-of-sight height direction, multiple missiles can conduct cooperative attacks along the line-of-sight height direction with the expected relative collision angle, avoiding continuous maneuvers to maintain a constant expected collision angle along the line-of-sight height direction, thereby reducing fuel consumption. By adopting an event-triggered mechanism along the line-of-sight height direction, the event-triggered cooperative guidance will not be updated and remains unchanged before the trigger condition is met, which can reduce the update frequency of the cooperative guidance command along the line-of-sight height direction, save the limited resources of the multi-missile system, and at the same time ensure a fast convergence speed and good guidance performance.

[0055] To achieve cooperative attacks of multiple missiles with the expected relative collision angle in the second direction, after constructing the cooperative guidance command and the first trigger mechanism in the first direction in step S1, enter step S2 to construct the cooperative guidance command and the second trigger mechanism in the second direction, specifically including:

[0056] Step S201, construct the consistency error of the relative line-of-sight angle in the second direction;

[0057] Step S202, construct the consistency error of the angular rate in the second direction;

[0058] Step S203, construct the tracking error of the angular rate in the second direction according to the consistency error of the relative line-of-sight angle in the second direction; construct the cooperative guidance command in the second direction according to the consistency error of the relative line-of-sight angle in the second direction, the consistency error of the angular rate in the second direction, and the tracking error of the angular rate in the second direction

[0059]

[0060] where, a Mβi (t) is the guidance command of the i-th missile in the second direction, α β1 , α β2 , α β3 , α β4 and μ β are positive constants, b β and c β are two positive odd numbers that satisfy b β / c β > 2, Υ i (t) is the consistency error of the relative line-of-sight angle of the i-th missile in the second direction, Ψ i (t) is the consistency error of the angular rate of the i-th missile in the second direction, e vβi(t) is the tracking error of the second direction angular rate of the i-th missile, p β and g β are two positive odd numbers that satisfy p β / g β > 1.

[0061] Step S204, construct a second triggering mechanism, and update the cooperative guidance command in the second direction according to the second triggering mechanism. The second triggering mechanism wherein,

[0062]

[0063] wherein, Θ βi (t) is the triggering error of the i-th missile in the second direction, 0 < η β < 1.

[0064] According to a specific embodiment of the present invention, the second direction is along the line-of-sight azimuth direction. The consistency error of the relative line-of-sight angle along the line-of-sight azimuth direction The consistency error of the angular rate of the azimuth direction relative to the line-of-sight angle

[0065] and the tracking error of the angular rate along the line-of-sight azimuth direction wherein, Υ i (t) is the consistency error of the i-th missile's relative line-of-sight angle along the line-of-sight azimuth direction, is the line-of-sight angle of the i-th missile along the line-of-sight azimuth direction and the expected line-of-sight angle of the i-th missile along the line-of-sight azimuth direction, is the line-of-sight angle of the j-th missile along the line-of-sight azimuth direction and the expected line-of-sight angle of the j-th missile along the line-of-sight azimuth direction, Ψ i (t) is the consistency error of the j-th missile's angular rate, q βi (t) is the line-of-sight angle of the i-th missile along the line-of-sight azimuth direction, qβ j (t) is the line-of-sight angle of the j-th missile along the line-of-sight azimuth direction, e vβi (t) is the tracking error of the i-th missile's angular rate along the line-of-sight azimuth direction, α β1 , α β2 and μ β are positive constants, b β and c β are two positive odd numbers that satisfy b β / c β > 2.

[0066] By applying this configuration method, through constructing a cooperative guidance command along the line-of-sight azimuth direction, only using the consistent error of the relative line-of-sight angle along the line-of-sight azimuth direction as the coordination variable to achieve spatial cooperative guidance along the line-of-sight azimuth direction, enabling multiple missiles to conduct cooperative attacks along the line-of-sight azimuth direction with the desired relative collision angle, avoiding continuous maneuvers to maintain a constant desired collision angle along the line-of-sight azimuth direction, thereby reducing fuel consumption. By adopting an event-triggered mechanism along the line-of-sight azimuth direction, the event-triggered cooperative guidance does not update and remains unchanged before the trigger condition is satisfied, which can reduce the update frequency of the cooperative guidance command along the line-of-sight azimuth direction, save the limited resources of the multi-missile system, and at the same time ensure a fast convergence speed and guarantee good guidance performance.

[0067] Through Step 1 and Step 2, the present invention pre-specifies the relative impact angle required for achieving spatial cooperative guidance between missiles. Since under certain interferences (such as unknown target maneuvers and model uncertainties), the relative impact angle on the target rarely changes significantly, it is actually unnecessary for the multi-missile system to continuously maneuver to maintain a constant required impact angle. Therefore, the cooperative guidance law of the present invention will be more flexible and can reduce fuel consumption. Under certain interferences (such as unknown target maneuvers and model uncertainties), the relative collision angle on the target rarely changes significantly, so the requirement for maintaining a constant desired collision angle can be relaxed, the adjustment frequency of the cooperative guidance command can be reduced, the fuel consumption can be reduced, and it is more flexible.

[0068] To enable multiple missiles to conduct cooperative attacks in time, after achieving the attack with the desired relative collision angle in Step S1 and Step S2, enter Step S3 to construct a cooperative guidance command along the line-of-sight direction and a trigger mechanism along the line-of-sight direction, specifically including:

[0069] Step S301, construct the consistency error of the remaining flight distance.

[0070] Step S302, construct the consistency error of the radial relative velocity.

[0071] Step S303, design a cooperative guidance command along the line-of-sight direction according to the consistency error of the remaining flight distance and the consistency error of the radial relative velocity.

[0072]

[0073] where, a Mri (t) is the guidance command of the i-th missile along the line-of-sight direction, α r1 , α r2 , α r3 , α r4 and μ r are all positive constants, b r and c r are two that satisfy br / c r A positive odd number greater than 2, Γ i (t) is the consistency error of the remaining flight distance of the i-th missile, α r3 , α r4 are all normal constants, t is the current time, is the triggering moment closest to the current time for the i-th missile, and is the next triggering moment of, e vri (t) is the velocity tracking error of the i-th missile, is the average value of the initial radial relative velocity, p r and g r are two positive odd numbers that satisfy p r / g r > 1.

[0074] Step S304, construct a line-of-sight triggering mechanism, and update the line-of-sight cooperative guidance command according to the line-of-sight triggering mechanism.

[0075] Line-of-sight triggering mechanism Among them,

[0076]

[0077] Among them, Θ ri (t) is the triggering error between the closest triggering state and the current state of the i-th missile, 0 < η r < 1.

[0078] The cooperative guidance commands in the line-of-sight elevation direction and the line-of-sight azimuth direction control multiple missiles to attack at a desired relative collision angle. The cooperative guidance command in the line-of-sight direction controls multiple missiles to achieve simultaneous attack. Any two of the line-of-sight elevation direction, the line-of-sight azimuth direction, and the line-of-sight direction are perpendicular to each other. The line-of-sight elevation direction triggering mechanism, the line-of-sight azimuth direction triggering mechanism, and the line-of-sight direction triggering mechanism are event-triggered.

[0079] Using this configuration method, an event-triggered robust nonlinear cooperative guidance command along the line of sight is designed. The remaining distance and the velocity along the line of sight are used as variables to coordinate and achieve time cooperative guidance. These variables can directly measure, avoiding the accuracy degradation caused by the remaining time estimation error, and maintaining stability at the same time. By using the event-triggered method and designing a suitable trigger mechanism, the cooperative guidance command does not update and remains unchanged before the trigger condition is satisfied, which can significantly reduce the update frequency of the cooperative guidance command and ensure the stability of the guidance system. To ensure a fast convergence speed, compared with the continuously updated time-triggered guidance law, the event-triggered guidance requires less computational effort, thus reducing the computational cost.

[0080] To further understand the present invention, the following combines Figures 1 to 6 A detailed description of an event-triggered simultaneous attack cooperative guidance method along the line of sight of the present invention is given.

[0081] Step S1: Construct a cooperative guidance command along the vertical direction of the line of sight and a trigger mechanism along the vertical direction of the line of sight, and update the cooperative guidance command along the vertical direction of the line of sight according to the trigger mechanism along the vertical direction of the line of sight, specifically including:

[0082] Step S101: Construct the consensus error of the relative line-of-sight angle along the vertical direction of the line of sight Ξ i (t) is the consensus error of the relative line-of-sight angle of the i-th missile along the vertical direction of the line of sight. i is a positive integer, j is a positive integer, i ∈ [1, N], j ∈ [1, N], N is the total number of missiles. When the i-th missile and the j-th missile can detect each other, a ij = 1, otherwise a ij = 0, t is the current time, is the deviation between the line-of-sight angle of the i-th missile along the vertical direction of the line of sight and the desired line-of-sight angle of the i-th missile along the vertical direction of the line of sight, is the deviation between the line-of-sight angle of the j-th missile in the vertical direction and the desired line-of-sight angle of the j-th missile in the vertical direction.

[0083] Step S102: Construct the consensus error of the angular rate along the vertical direction of the line of sight Π i (t) is the consensus error of the angular rate of the i-th missile along the vertical direction of the line of sight, q εi (t) is the line-of-sight angle of the i-th missile along the vertical direction of the line of sight, q εj (t) is the line-of-sight angle of the j-th missile along the vertical direction of the line of sight.

[0084] Step S103: Construct the tracking error of the angular rate along the vertical direction of the line of sight according to the consensus error of the relative line-of-sight angle along the vertical direction of the line of sight e vεi (t) is the tracking error of the angular rate of the i-th missile in the line-of-sight elevation direction, α ε1 、α ε2 and μ ε are all positive constants, b ε and c ε are two positive odd numbers satisfying b ε / c ε > 2.

[0085] Step S104, construct the cooperative guidance command in the line-of-sight elevation direction according to the consistency error of the relative line-of-sight angle in the line-of-sight elevation direction, the consistency error of the angular rate in the line-of-sight elevation direction, and the tracking error of the angular rate in the line-of-sight elevation direction

[0086]

[0087] where a Mεi (t) is the guidance command of the i-th missile in the line-of-sight elevation direction, r i (t) is the relative distance between the i-th missile and the target, t is the current time, q εi (t) is the line-of-sight angle of the i-th missile in the line-of-sight elevation direction, q βi (t) is the line-of-sight angle of the i-th missile in the line-of-sight azimuth direction, α ε1 、α ε2 、α ε3 、α ε4 and μ ε are all positive constants, b ε and c ε are two positive odd numbers satisfying b ε / c ε > 2, is the trigger time closest to the current time for the i-th missile, and is 's next trigger time. Π i (t) is the consistency error of the angular rate of the i-th missile in the line-of-sight azimuth direction, e vεi (t) is the tracking error of the angular rate of the i-th missile in the line-of-sight elevation direction, p ε and g ε are two positive odd numbers satisfying p ε / g ε > 1.

[0088] Construct a trigger mechanism in the line-of-sight elevation direction, and update the cooperative guidance command in the line-of-sight elevation direction according to the trigger mechanism in the line-of-sight elevation direction,

[0089]

[0090] where, Θ εi (t) is the triggering error of the i-th missile in the first direction, 0 < η ε < 1.

[0091] Step S2, construct a cooperative guidance command and a triggering mechanism along the line-of-sight azimuth direction, specifically including:

[0092] Step S201, construct the consistency error of the relative line-of-sight angle along the line-of-sight azimuth direction Υ i (t) is the consistency error of the relative line-of-sight angle of the i-th missile along the line-of-sight azimuth direction, is the deviation between the line-of-sight angle of the i-th missile along the line-of-sight azimuth direction and the expected line-of-sight angle of the i-th missile along the line-of-sight azimuth direction, is the deviation between the line-of-sight angle of the j-th missile along the line-of-sight azimuth direction and the expected line-of-sight angle of the j-th missile along the line-of-sight azimuth direction.

[0093] Step S202, construct the consistency error of the angular rate along the line-of-sight azimuth direction Ψ i (t) is the consistency error of the angular rate of the j-th missile along the line-of-sight azimuth direction, q βi (t) is the line-of-sight angle of the i-th missile along the line-of-sight azimuth direction, q βj (t) is the line-of-sight angle of the j-th missile along the line-of-sight azimuth direction.

[0094] Step S203, construct the tracking error of the angular rate along the line-of-sight azimuth direction according to the consistency error of the relative line-of-sight angle along the line-of-sight azimuth direction e vβi (t) is the tracking error of the angular rate of the i-th missile along the line-of-sight azimuth direction, α β1 , α β2 and μ β are positive constants, b β and c β are two positive odd numbers that satisfy b β / c β > 2.

[0095] Construct a cooperative guidance command along the line-of-sight azimuth direction according to the consistency error of the relative line-of-sight angle along the line-of-sight azimuth direction, the consistency error of the angular rate along the line-of-sight azimuth direction, and the tracking error of the angular rate along the line-of-sight azimuth direction

[0096]

[0097] where, a Mβi (t) is the guidance command of the i-th missile in the line-of-sight azimuth direction, α β1 , α β2 , αβ3 , α β4 and μ β are normal constants, b β and c β are two positive odd numbers satisfying b β / c β > 2, Υ i (t) is the consistency error of the i-th missile's relative line-of-sight angle along the line-of-sight azimuth direction, Ψ i (t) is the consistency error of the i-th missile's angular rate along the line-of-sight azimuth direction, e vβi (t) is the tracking error of the i-th missile's angular rate along the line-of-sight azimuth direction, p β and g β are two positive odd numbers satisfying p β / g β > 1.

[0098] Step S204, construct a triggering mechanism along the line-of-sight azimuth, and update the cooperative guidance command along the line-of-sight azimuth direction according to the triggering mechanism along the line-of-sight azimuth. The triggering mechanism along the line-of-sight azimuth

[0099]

[0100] where, Θ βi (t) is the triggering error of the i-th missile along the line-of-sight azimuth, 0 < η β < 1.

[0101] Step S3, construct a cooperative guidance command along the line-of-sight direction and a triggering mechanism along the line-of-sight direction, specifically including:

[0102] Step S301, construct the consistency error of the remaining flight distance where, Γ i (t) is the consistency error of the remaining flight distance of the i-th missile, r i (t) is the relative distance between the i-th missile and the target, r j (t) is the relative distance between the j-th missile and the target.

[0103] Step S302, construct the consistency error of the radial relative velocity where, Λ i (t) is the consistency error of the radial relative velocity of the i-th missile, v ri (t) is the radial relative velocity of the i-th missile, v rj (t) is the radial relative velocity of the j-th missile.

[0104] Step S303, design a cooperative guidance command along the line-of-sight direction according to the consistency error of the remaining flight distance and the consistency error of the radial relative velocity,

[0105]

[0106] where a Mri (t) is the guidance command of the i-th missile along the line of sight, and α r1 , α r2 , α r3 , α r4 and μ r are all positive constants, b r and c r are two positive odd numbers satisfying b r / c r > 2, and Γ i (t) is the consistency error of the remaining flight distance of the i-th missile, and α r3 , α r4 are all positive constants, t is the current time, is the triggering moment closest to the current time for the i-th missile, and is 's next triggering moment, and e vri (t) is the velocity tracking error of the i-th missile,

[0107] is the average value of the initial radial relative velocity, and p r and g r are two positive odd numbers satisfying p r / g r > 1.

[0108] Step S304: Construct a triggering mechanism along the line of sight, and update the cooperative guidance command along the line of sight according to the triggering mechanism along the line of sight.

[0109] Triggering mechanism along the line of sight where

[0110]

[0111] where Θ ri (t) is the triggering error between the nearest triggering state and the current state of the i-th missile, and 0 < η r < 1.

[0112] As Figure 1 and Figure 2 shown, where Figure 2In this case, Ts is the guidance period. In the present invention, the cooperative guidance commands in the line-of-sight elevation direction and the cooperative guidance commands in the line-of-sight azimuth direction control multiple missiles to attack with a desired relative collision angle. The cooperative guidance commands in the line-of-sight direction control multiple missiles to achieve simultaneous attack. Any two of the line-of-sight elevation direction, the line-of-sight azimuth direction, and the line-of-sight direction are perpendicular to each other. The triggering mechanisms in the line-of-sight elevation direction, the line-of-sight azimuth direction, and the line-of-sight direction are event-triggered.

[0113] Four missiles are used for cooperative target attack. As Figure 3 shown, the miss distances and attack times of the four missiles finally reach consistency. According to the simulation results, as Figures 4 to 6 shown, where TT is time-triggered, ET is event-triggered, M1, M2, M3, and M4 correspond to Missile 1, Missile 2, Missile 3, and Missile 4 respectively. The flight time of the missiles in the scenario is 13.766 s, and the simulation step size is selected as 0.001 s. Therefore, the update times of time-triggered guidance are 13,766. Using the proposed event-triggered guidance scheme, the trigger times can be reduced by more than 65% to 4,800 times (for example, the line-of-sight direction trigger times of Missile 4). For the line-of-sight azimuth direction of Missile 3, it can even be reduced to only 40 times (about 0.3% of the time-triggered update quantity). It can be seen from this that the event-triggered cooperative guidance scheme can greatly reduce the update frequency of guidance commands.

[0114] In summary, the three-dimensional event-triggered cooperative guidance method of the present invention proposes a three-dimensional event-triggered fixed-time cooperative guidance law with relative collision angle constraints, which can improve the flexibility of the cooperative guidance law considering collision angle constraints and reduce the computational burden. By formulating the guidance laws in the line-of-sight direction and perpendicular to the line-of-sight direction, in the line-of-sight direction, the remaining distance and the velocity along the line of sight are used as variables to coordinate the time-to-go guidance, avoiding the reduction of accuracy due to the remaining time estimation error, especially suitable for maneuvering targets. Perpendicular to the line-of-sight direction, instead of specifying a specific desired collision angle for each missile, only the consistent error of the relative collision angle is used as a coordination variable to achieve spatial cooperative guidance, so as to avoid continuous maneuvers to maintain a constant desired collision angle, thereby reducing fuel consumption. The event-triggered mechanism is adopted to reduce the update frequency of cooperative guidance commands. To ensure the convergence speed of the guidance error, the fixed-time control theory is used. The proposed event-triggered cooperative guidance law has good stability, and at the same time, it can ensure that there is no Zeno behavior (Zeno behavior means that an infinite number of events are triggered within a finite time interval) when implementing the proposed event-triggered cooperative guidance law. Numerical simulations show that the guidance law and trigger mechanism of the present invention achieve strict simultaneous attack and satisfy the relative collision angle constraints. The proposed event-triggered cooperative guidance law with relative collision angle constraints reduces the computational burden of cooperative guidance commands and reduces fuel consumption.

Claims

1. A three-dimensional event-triggered cooperative guidance method, characterized in that It includes the following steps: Step 1: Construct the cooperative guidance command in the first direction and the first trigger mechanism, and update the cooperative guidance command in the first direction according to the first trigger mechanism; Step 2: Construct the cooperative guidance command in the second direction and the second trigger mechanism, and update the cooperative guidance command in the second direction according to the second trigger mechanism; Step 3: Construct the cooperative guidance command in the third direction and the third trigger mechanism, and update the cooperative guidance command in the third direction according to the third trigger mechanism; Among them, the cooperative guidance commands in the first direction and the second direction control multiple missiles to attack at a desired relative collision angle, the cooperative guidance command in the third direction controls multiple missiles to achieve simultaneous attack, any two of the first direction, the second direction and the third direction are perpendicular to each other, and at least one of the first trigger mechanism, the second trigger mechanism and the third trigger mechanism is event-triggered; Among them, the first triggering mechanism is: Θ εi (t) is the triggering error of the i-th missile in the first direction, 0 < η ε < 1; Cooperative guidance command in the first direction: where a Mεi (t) is the guidance command of the i-th missile in the first direction, ri(t) is the relative distance between the i-th missile and the target, t is the current time, q ε i(t) is the line-of-sight angle of the i-th missile in the first direction, q βi (t) is the line-of-sight angle of the i-th missile in the second direction, α ε1 、α ε2 、α ε3 、α ε4 and μ ε are all positive constants, b ε and c ε are two positive odd numbers satisfying b ε / c ε > 2, is the triggering moment closest to the current time for the i-th missile, and is 's next triggering moment, Ξ i (t) is the consensus error of the relative line-of-sight angle of the i-th missile in the first direction; Π i (t) is the consensus error of the angular rate of the i-th missile in the first direction, e vεi (t) is the tracking error of the angular rate of the i-th missile in the first direction, p ε and g ε are two positive odd numbers satisfying p ε / g ε > 1.

2. The three-dimensional event-triggered cooperative guidance method according to claim 1, wherein: The first direction is along the line-of-sight elevation direction, the second direction is along the line-of-sight azimuth direction, and the third direction is along the line-of-sight direction.

3. The three-dimensional event-triggered cooperative guidance method according to claim 1, characterized in that: Specifically constructing the cooperative guidance command in the first direction includes: constructing the consistency error of the relative line-of-sight angle in the first direction; constructing the consistency error of the angular rate in the first direction; constructing the tracking error of the angular rate in the first direction according to the consistency error of the relative line-of-sight angle in the first direction; constructing the cooperative guidance command in the first direction according to the consistency error of the relative line-of-sight angle in the first direction, the consistency error of the angular rate in the first direction and the tracking error of the angular rate in the first direction.

4. The three-dimensional event-triggered cooperative guidance method according to claim 1, characterized in that: Specifically constructing the cooperative guidance command in the second direction includes: constructing the consistency error of the relative line-of-sight angle in the second direction; constructing the consistency error of the angular rate in the second direction; constructing the tracking error of the angular rate in the second direction according to the consistency error of the relative line-of-sight angle in the second direction; constructing the cooperative guidance command in the second direction according to the consistency error of the relative line-of-sight angle in the second direction, the consistency error of the angular rate in the second direction and the tracking error of the angular rate in the second direction.

5. The three-dimensional event-triggered cooperative guidance method according to claim 1, characterized in that: Specifically constructing the cooperative guidance command in the third direction includes: constructing the consistency error of the remaining flight distance; constructing the consistency error of the radial relative velocity; designing the cooperative guidance command in the third direction according to the consistency error of the remaining flight distance and the consistency error of the radial relative velocity.

6. The three-dimensional event-triggered cooperative guidance method according to claim 1 or 4, characterized in that: Cooperative guidance command in the second direction: Among them, a Mβi (t) is the guidance command of the i-th missile in the second direction, α β1 , α β2 , α β3 , α β4 and μ β are positive constants, b β and c β are two positive odd numbers that satisfy b β / c β > 2, Υ i (t) is the consistency error of the relative line-of-sight angle of the i-th missile in the second direction, Ψ i (t) is the consistency error of the angular rate of the i-th missile in the second direction, ev β i(t) is the tracking error of the angular rate of the i-th missile in the second direction, p β and g β are two positive odd numbers that satisfy p β / g β > 1.

7. The three-dimensional event-triggered cooperative guidance method according to claim 1 or 5, characterized in that: Cooperative guidance command in the third direction where a Mri (t) is the guidance command of the i-th missile along the line of sight, α r1 , α r2 , α r3 , α r4 and μ r are all positive constants, b r and c r are two positive odd numbers satisfying b r / c r > 2, Γ i (t) is the consistency error of the remaining flight distance of the i-th missile, α r3 , α r4 are all positive constants, t is the current time, is the triggering moment closest to the current time for the i-th missile, and is 's next triggering moment, Λ i (t) is the consistency error of the radial relative velocity of the i-th missile, e vri (t) is the velocity tracking error of the i-th missile, p r and g r are two positive odd numbers satisfying p r / g r > 1.

8. The three-dimensional event-triggered cooperative guidance method according to claim 1, wherein: In the first trigger mechanism, 9. The three-dimensional event-triggered cooperative guidance method according to claim 6, wherein: Second trigger mechanism Among them, Θ βi (t) is the triggering error of the i-th missile in the second direction, 0 < η β < 1.

10. The three-dimensional event-triggered cooperative guidance method according to claim 7, characterized in that: Third trigger mechanism Among them, Among them, Θ ri (t) is the triggering error between the most recent triggering state and the current state of the i-th missile, 0 < η r < 1.

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