Multi-vehicle cooperative guidance method satisfying impact angle constraint in three-dimensional space

Abstract

The application discloses a multi-aircraft cooperative guidance method meeting a falling angle constraint in a three-dimensional space. In the method, a three-dimensional falling angle constraint guidance law is proposed for each aircraft, and an explicit residual flight time estimation method is given. Then, the above guidance law is taken as a basic guidance law, the residual flight time estimation value is taken as a coordination variable, and a bias instruction for residual flight time consistency adjustment is additionally added, so that the multi-aircraft reaches the target position in a specified direction at the same time.

Description

TECHNICAL FIELD

[0001] The present application relates to a multi-vehicle cooperative guidance method, in particular to a multi-vehicle cooperative guidance method capable of reaching a target position with a specified impact angle in three-dimensional space. BACKGROUND

[0002] With the rapid development of information and electronic technology, the concept of multi-vehicle cooperative guidance has been paid more and more attention in recent years. Compared with single-vehicle independent guidance, multi-vehicle cooperative guidance can improve the ability and efficiency of completing complex tasks by achieving simultaneous arrival at a specified target position. In particular, in the military field, multi-vehicle cooperative guidance technology is an effective means to saturate enemy defense systems and improve the penetration capability of weapon systems. Therefore, multi-vehicle cooperative guidance has important practical significance.

[0003] The main purpose of cooperative guidance is to achieve simultaneous arrival. In addition, in order to meet specific target tasks, additional impact angle constraints need to be met. For example, in the military field, in order to improve the penetration capability of hard targets such as armored vehicles or deeply buried targets, it is necessary to hit the weak part of the target with a specified impact angle. Therefore, it is urgent to design a multi-vehicle three-dimensional cooperative guidance law that can simultaneously achieve impact angle constraints and simultaneous arrival.

[0004] However, impact angle constraints and simultaneous arrival are two different spatiotemporal constraint conditions, and there is a strong coupling relationship between them. Moreover, since the tangential acceleration of most vehicles in practice cannot be autonomously adjusted on demand, the cooperative guidance problem of achieving impact angle constraints and simultaneous arrival is a highly underactuated problem, which requires only the normal acceleration of the vehicle to be designed to meet multiple terminal constraint conditions. In addition, the high nonlinearity of the three-dimensional guidance model further increases the difficulty of solving this problem. Therefore, there is still little research on this aspect.

[0005] Due to the above reasons, the present inventors have conducted in-depth research on the problem of multi-vehicle cooperative guidance in order to design a multi-vehicle cooperative guidance method capable of reaching a target position with a specified impact angle in three-dimensional space. SUMMARY

[0006] In order to overcome the above problems, the present inventors have made intensive research and designed a multi-vehicle cooperative guidance method that meets impact angle constraints in three-dimensional space. In this method, a three-dimensional impact angle constraint guidance law is first proposed for each vehicle, and an explicit residual flight time estimation method is given. Then, the above guidance law is used as the basic guidance law, and the residual flight time estimation value is used as the coordination variable. By additionally adding a bias command for residual flight time consistency adjustment, the present application is completed.

[0007] Specifically, the application aims to provide a multi-aircraft cooperative guidance method under three-dimensional space meeting the impact angle constraint,

[0008] In the method, the aircraft is controlled to fly to the target through three-dimensional impact angle constraint guidance instructions, wherein the three-dimensional impact angle constraint guidance instructions comprise position adjustment instructions for controlling the aircraft to accurately reach and angle adjustment instructions for controlling the aircraft to meet the impact angle constraint.

[0009] A bias term for time of flight consistency adjustment is added in the position adjustment instructions.

[0010] The application has the following beneficial effects:

[0011] (1) The multi-aircraft cooperative guidance method under three-dimensional space meeting the impact angle constraint provided by the application can enable each aircraft to reach the target position with a specified impact angle in three-dimensional space, without involving complex mathematical operations, and is simple in form and easy to implement.

[0012] (2) The multi-aircraft cooperative guidance method under three-dimensional space meeting the impact angle constraint provided by the application can give real-time estimation of the residual flight time of each aircraft under the above impact angle constraint guidance law, and has high estimation accuracy.

[0013] (3) The multi-aircraft cooperative guidance method under three-dimensional space meeting the impact angle constraint provided by the application can enable multiple aircraft to reach the target position with a specified impact angle in three-dimensional space only by applying normal guidance instructions, and has good performance and application potential. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 A guidance geometric relationship between the aircraft and the target position in the application is shown.

[0015] Figure 2 A communication topology relationship between the five aircraft in the experimental example of the application is shown.

[0016] Figure 3 A flight trajectory curve of the five aircraft in three-dimensional space in the experimental example of the application is shown.

[0017] Figure 4 A field of view angle change curve of the five aircraft in the experimental example of the application is shown.

[0018] Figure 5 A change curve of the included angle between the current speed and the expected terminal speed of the five aircraft in the experimental example of the application is shown.

[0019] Figure 6 A residual flight time change curve of the five aircraft in the experimental example of the application is shown.

[0020] Figure 7 Fig. 1 shows the amplitude variation curves of the cooperative guidance instructions of five aircraft in the experimental example of the present application. DETAILED DESCRIPTION

[0021] The present application will be further described by the accompanying drawings and examples. The features and advantages of the present application will become more apparent from the description.

[0022] The word "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 stated otherwise, the drawings are not drawn to scale and the disclosure is not limited to the specific embodiments illustrated in the drawings.

[0023] A method for cooperative guidance of multiple aircrafts under three-dimensional space with impact angle constraint is provided according to the present application;

[0024] In the method, the aircrafts are controlled to fly towards the target by three-dimensional impact angle constraint cooperative guidance instructions, wherein the three-dimensional impact angle constraint guidance instructions include position adjustment instructions for controlling the aircrafts to accurately reach the target and angle adjustment instructions for controlling the aircrafts to meet the impact angle constraint;

[0025] A bias term for time-of-flight consistency adjustment is added in the position adjustment instructions.

[0026] Preferably, the position adjustment instructions are obtained by the following formula (eight):

[0027]

[0028] The angle adjustment instructions are obtained by the following formula (nine):

[0029]

[0030] The bias term a t,i is obtained by the following formula (ten):

[0031]

[0032] Preferably, the three-dimensional impact angle constraint cooperative guidance instructions are obtained by the following formula (one):

[0033]

[0034] wherein a i represents the guidance instructions of the i-th aircraft,

[0035] V i represents the speed of the i-th aircraft; Figure 1 The guidance geometry between the aircraft and the target position is shown in the figure;

[0036] R i represents the relative distance between the i-th aircraft and the target position; represents the line-of-sight vector between the i-th aircraft and the target position; It is obtained in real time by a seeker carried on the aircraft, such as a laser seeker or an image seeker.

[0037] N, K and K represent guidance parameters; preferably, N = 4, K = 2, K = 10 are taken;

[0038] σ i represents the field of view angle of the i-th aircraft;

[0039] ∈ i represents the error angle of the i-th aircraft;

[0040] v i represents the unit vector of ; represents the velocity vector of the i-th aircraft, It is obtained in real time by a sensor carried on the aircraft, such as a satellite signal receiver or an inertial navigation module;

[0041] α i represents the unit vector perpendicular to the line-of-sight of the missile and the velocity of the aircraft;

[0042] γ i represents the unit vector perpendicular to the line-of-sight of the missile and the desired terminal velocity;

[0043] Preferably,

[0044] ψ(ξ i ) represents a function of ξ i ;

[0045] ξ i represents the auxiliary angle of the i-th aircraft;

[0046] t go,i represents the remaining flight time of the i-th aircraft;

[0047] e i represents the local error of the remaining flight time of the i-th aircraft.

[0048] Preferably, the auxiliary angle ξ i of the i-th aircraft is obtained by the following formula (two):

[0049]

[0050] Preferably, ψ(ξ i ) represents a function of ξ i , as shown in the following formula (three);

[0051]

[0052] wherein ξ m is a preset normal number, and its value is 0.5°-3°, preferably 1°; m is an integer, and m>1, preferably m=2.

[0053] In the present application, ψ(ξ i ) is set to avoid the singular problem of the guidance command when the auxiliary angle ξ i approaches zero.

[0054]

[0055] When the auxiliary angle ξ i approaches zero, the bias command a t,i tends to zero.

[0056] In the present application, cosσ i in the numerator of formula (ten) is used to avoid that σ i exceeds 90 degrees during the guidance process. For the proposed cooperative guidance command formula (one), the following formula (eleven) is established,

[0057]

[0058] Therefore, as long as the initial value of σ i is less than 90 degrees, the cooperative guidance command formula (one) can ensure that σ i is always less than 90 degrees throughout the guidance process, i.e., gradually reduces the relative distance between the aircraft and the target position, which is advantageous for practical application. On the one hand, it can avoid the cooperative failure caused by the aircraft moving away from the target position during the guidance process, and on the other hand, it can avoid the failure to obtain guidance information caused by the target position being located outside the field of view of the onboard sensor.

[0059] Preferably, the remaining flight time t go,i of the i-th aircraft is obtained by the following formula (four):

[0060]

[0061] In the derivation process of formula (four) in the present application, the small angle assumption is involved, but the explicit real-time estimation method of the remaining flight time provided by formula (four) is easy to implement in engineering, and through experiments it can be verified that even when σ i and δ i are large, the estimation accuracy of formula (four) is still high, which can meet the guidance control requirements. The δ i= arccos (a i · r i ) represents the included angle between unit vectors a i and r i .

[0062] The local error e i of the remaining flight time of the i-th aircraft is obtained by the following equation (five):

[0063]

[0064] where a ij = 1 if the i-th aircraft can receive the information of the j-th aircraft, otherwise a ij = 0;

[0065] M represents the total number of aircrafts;

[0066] j represents the j-th aircraft;

[0067] t go,j represents the remaining flight time of the j-th aircraft, which is obtained by the j-th aircraft itself in real time and is transmitted by the j-th aircraft to other aircrafts that can be connected to the signal of the j-th aircraft in real time. That is, in this method, multiple aircrafts synchronously estimate their own remaining flight time and transmit the estimation results in real time, while also receiving the remaining estimated time transmitted by other aircrafts. Whether the information transmission between multiple aircrafts can be completed depends on the distance between them and the stability of the transmitted signal. Only when at least one stable signal connection with another aircraft is formed, the aircraft can become a member of the cooperative aircraft group and finally achieve that all aircrafts in the cooperative aircraft group hit the target at the same time.

[0068] In a preferred embodiment, the field of view angle σ i of the i-th aircraft is obtained by the following equation (six):

[0069] σ i = arccos (v i · r i ) (six)

[0070] where r i represents the unit vector of v , and r represents the line of sight vector between the i-th aircraft and the target position. In this application, the field of view angle σ i is zeroized to control the aircraft to accurately reach the predetermined position, and the error angle ∈ i is zeroized to control the aircraft to meet the landing angle constraint.

[0071] The error angle ∈ i of the i-th aircraft is obtained by the following equation (seven):

[0072] ∈ i = arccos(r i ·u i )(seven)

[0073] wherein u i represents a unit vector of , and represents a desired terminal speed of the i-th aircraft, which is determined by a desired landing angle.

[0074] In a preferred embodiment, the closed-loop stability of the provided cooperative guidance law can be guaranteed by consensus theory, and the consensus convergence time of the remaining flight time error can be adjusted by changing the value of κ, the greater the value of κ, the faster the convergence time.

[0075] In practical applications, the spatial guidance command obtained from equation (one) needs to be further decomposed into the velocity coordinate system, which can be decomposed by the following equation (twelve):

[0076]

[0077] wherein a y,i represents a guidance command component of the yaw channel of the i-th aircraft, and a z,i represents a guidance command component of the pitch channel of the i-th aircraft; in this application, each aircraft specifically controls the rudder work of the rudder by a y,i and a z,i . Multiple aircrafts can all reach the target position with a specified landing angle along their respective flight trajectories.

[0078] j V,i represents a unit direction vector of the Y-axis of the velocity coordinate system of the i-th aircraft;

[0079] k V,i represents a unit direction vector of the Z-axis of the velocity coordinate system of the i-th aircraft;

[0080] k I is defined as a unit direction vector of the Z-axis of the inertial coordinate system XYZ, if ||V i × k I ‖≠0, then k V,i is determined by the following equation:

[0081]

[0082] If k V,i can be selected as any unit vector located in the horizontal plane, and then j V,i is determined by the right-hand rule, that is, j V,i = k V,iXv i .

[0083] Experimental Example

[0084] The guidance scene of five aircrafts numbered 1-5 reaching the origin position with specified impact angle in three-dimensional space is simulated, and the guidance instructions of each aircraft are calculated according to the multi-aircraft cooperative guidance method provided in this application which meets the impact angle constraint in three-dimensional space, that is, the control instruction of each aircraft is obtained by the following formula (I):

[0085]

[0086] Wherein, a i represents the guidance instruction of the i-th aircraft,

[0087] V i represents the speed of the i-th aircraft;

[0088] R i represents the relative distance between the i-th aircraft and the target position;

[0089] N, K and κ all represent guidance parameters, N = 4, K = 2, κ = 10;

[0090] σ i represents the field of view angle of the i-th aircraft;

[0091] ∈ i represents the error angle of the i-th aircraft;

[0092] v i represents unit vector; represents the velocity vector of the i-th aircraft;

[0093] α i represents the unit vector perpendicular to the line of sight of the missile and the aircraft speed;

[0094] γ i represents the unit vector perpendicular to the line of sight of the missile and the desired terminal speed;

[0095] ψ(ξ i ) represents a function of ξ i ;

[0096] ξ i represents the auxiliary angle of the i-th aircraft;

[0097] t go,i the remaining flight time of the i-th aircraft;

[0098] e i represents the local error of the remaining flight time of the i-th aircraft.

[0099] the assistance angle of the i-th aircraft i is obtained by the following formula (two) :

[0100]

[0101] ψ(ξ i ) represents a function of ξ i , as shown in the following formula (three) ;

[0102]

[0103] wherein ξ m = 1°; m = 2.

[0104] the remaining flight time of the i-th aircraft t go,i is obtained by the following formula (four) :

[0105]

[0106] the local error of the remaining flight time of the i-th aircraft e i is obtained by the following formula (five) :

[0107]

[0108] wherein if the i-th aircraft can receive the information of the j-th aircraft, then a ij = 1, otherwise a ij = 0;

[0109] M represents the total number of aircrafts, and is 5;

[0110] j represents the j-th aircraft;

[0111] t go,j represents the remaining flight time of the j-th aircraft.

[0112] The communication topology relationship among the 5 aircrafts is shown in Figure 2 .

[0113] In this experimental example, the initial conditions and the expected landing angles of the aircrafts are shown in Table 1, wherein the high-low angle represents the included angle between the velocity vector and the horizontal plane, and the azimuth angle represents the included angle between the projection of the velocity vector on the horizontal plane and the X axis, when the high-low angle is -90 degrees, the corresponding azimuth angle is undefined.

[0114] Table 1 Simulation conditions of the 5 aircrafts in the experimental example

[0115]

[0116]

[0117] In the experimental example, the following results are obtained through simulation:

[0118] The flight trajectory curves of 5 aircraft in three-dimensional space, such as Figure 3 As shown in;

[0119] The field of view angle of the five aircraft changes with time, such as Figure 4 As shown in;

[0120] The angle between the current velocity of the five aircraft and the desired terminal velocity, i.e., ε imp,i =arccos(v i ·u i ), the time-varying curve, such as Figure 5 As shown in;

[0121] The remaining flight time variation curves of the five aircraft are as follows: Figure 6 As shown in;

[0122] The curve of the coordinated guidance command amplitude of the five aircraft changing with time is as follows: Figure 7 As shown in .

[0123] The curve for the first aircraft is represented in the figure by a solid line with a circular pattern;

[0124] The curve of the second aircraft is indicated in the figure by a dotted line with a triangular pattern;

[0125] The curve of the third aircraft is indicated in the figure by a dot-dashed line with a diamond pattern;

[0126] The curve for the fourth aircraft is indicated in the figure by a dotted line with a square pattern;

[0127] The curve of the fifth aircraft is represented in the figure by a solid line with a five-pointed star pattern;

[0128] Depend on Figure 3 It can be seen that although the initial conditions of each aircraft are very different, after using the method provided in this application, multiple aircraft can reach the target position at the same time with high precision and specified landing angle in three-dimensional space.

[0129] Depend on Figure 4 It can be seen that the field of view angle of each aircraft does not exceed 90 degrees throughout the guidance process and finally converges to zero, that is, the speed direction of the aircraft will eventually point to the target. This result is beneficial to improving the terminal position accuracy and reducing the terminal energy consumption.

[0130] Depend on Figure 5 It can be seen that under the action of the provided cooperative guidance law, the angle between the current flight speed of each aircraft and the desired terminal speed converges to zero, that is, the specified landing angle constraint conditions are finally satisfied.

[0131] Depend on Figure 6 It can be seen that the provided cooperative guidance law can achieve consistent convergence of the remaining flight time in a relatively short period of time, and after the error converges, the bias term in the cooperative guidance method is zero. The remaining flight time estimation method provided by the present invention can ultimately achieve the goal of accurately reaching the target position at the same time.

[0132] Depend on Figure 7 It can be seen that each aircraft maintains a small guidance command amplitude throughout the guidance process, among which the initial guidance command is relatively large to achieve rapid convergence of the remaining flight time error. Subsequently, the bias term is zero, and the guidance command is maintained in a smaller amplitude range to meet the landing angle constraint. Finally, the guidance command converges to zero, and the energy consumption is reasonably distributed, which is conducive to engineering applications.

[0133] From the above results, it can be seen that the multi-aircraft collaborative guidance method that meets the angle of impact constraint in three-dimensional space provided in this application can control multiple aircraft to hit the target simultaneously according to the predetermined angle of impact.

[0134] 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 method for multi-vehicle cooperative guidance under three-dimensional space with impact angle constraint, characterized in that: In the method, the vehicles are controlled to fly towards the target through three-dimensional impact angle constraint guidance instructions, wherein the three-dimensional impact angle constraint guidance instructions comprise position adjustment instructions for controlling the vehicles to accurately reach the target and angle adjustment instructions for controlling the vehicles to meet the impact angle constraint; A bias term for time-of-flight consistency adjustment is added in the position adjustment instructions; The three-dimensional impact angle constraint cooperative guidance instructions are obtained through the following formula (I): where a i represents the guidance command for the i-th aircraft, V i denotes the speed magnitude of the i-th aircraft; R i represents the relative distance between the ith aircraft and the target position; N, K and κ all represent guidance parameters; σ i denotes the field of view angle of the i-th aircraft; ∈ i denotes the error angle of the i-th aircraft; v i a unit vector of a unit vector of a velocity vector of the i-th aircraft a i represents a unit vector perpendicular to the line of sight and the speed of the aircraft; gamma i denotes the unit vector perpendicular to the line of sight of the projectile and the desired terminal velocity; ψ(ξ i ) denotes a function of ξ i ; ξ i denotes the auxiliary angle of the i-th aircraft; t go,i remaining flight time of the ith aircraft; e i denotes the local error of the remaining flight time of the i-th aircraft; The remaining flight time t of the i-th aircraft go,i is obtained by the following equation (four): local error e of the remaining flight time of the i-th aircraft i is obtained by the following equation (five) wherein, if the i-th aircraft can receive the information of the j-th aircraft, then a ij = 1, otherwise a ij = 0; M represents the total number of vehicles; j represents the jth vehicle; t go,j represents the remaining flight time of the jth aircraft. 2.The method for multi-vehicle cooperative guidance under three-dimensional space with impact angle constraint according to claim 1, characterized in that: the auxiliary angle ξ of the i-th aircraft i is obtained by the following equation (two): 3.The method for multi-vehicle cooperative guidance under three-dimensional space with impact angle constraint according to claim 1, characterized in that: ψ(ξ i ) represents a function of ξ i , as shown in Equation (three) below; wherein ξ m is a predetermined positive number; m is an integer, and m > 1. 4.The method for multi-vehicle cooperative guidance under three-dimensional space with impact angle constraint according to claim 1, characterized in that: the field of view angle σ of the ith aerial vehicle i is obtained by the following equation (six) σ i = arccos(v i · r i )(six) where r i represents a unit vector, represents the line-of-sight vector between the ith aircraft and the target location. 5.The method for multi-vehicle cooperative guidance under three-dimensional space with impact angle constraint according to claim 1, characterized in that: error angle ∈ of the i-th aircraft i is obtained by the following equation (seven) ∈ i = arccos(r i · u i )(seven) where u i represents a unit vector, represents the desired terminal velocity of the i-th aircraft.

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