Multi-vehicle cooperative terminal guidance method with line-of-sight separation angle constraint

Abstract

This invention discloses a multi-vehicle cooperative terminal guidance method and related products with line-of-sight separation angle constraints. Both the lead and follower aircraft generate the lead aircraft's line-of-sight tilt tracking error, line-of-sight tilt velocity tracking error, line-of-sight deflection tracking error, line-of-sight deflection velocity tracking error, sliding mode surface function related to the line-of-sight tilt tracking error, and sliding mode surface function related to the line-of-sight deflection tracking error based on the command polynomial coefficients and set equations; thereby determining the normal acceleration command and the lateral acceleration command. This method can achieve line-of-sight separation angle constraints.

Description

Technical Field

[0001] This invention relates to a multi-vehicle cooperative terminal guidance method with line-of-sight separation angle constraints and related products. Background Technology

[0002] For representative infrared or passive radar guidance modes, a single aircraft only provides target measurement information in terms of line-of-sight angle and line-of-sight angular velocity, lacking missile-target distance information. This leads to the inability to estimate remaining flight time, making coordinated attacks on targets difficult. Dual-line-of-sight localization is an important way to compensate for the insufficient target information obtained by a single aircraft. The basic principle is that two aircraft communicate in real time and acquire each other's status information. In the detection triangle formed by the two aircraft and the target, three angles and the length of the side of the line connecting the two aircraft can be determined, and then the target's position information can be obtained using the sine theorem. The line-of-sight separation angle between the two aircraft and the target (i.e., the angle between the missile-target line-of-sight vectors of the two aircraft) has a decisive impact on the target localization accuracy. When the two aircraft are collinear or nearly collinear with the target, the target localization error increases sharply, and the dual-line-of-sight localization method fails.

[0003] Chinese patent CN112525003B proposes an extended proportional guidance method with landing angle constraints. The method includes the following steps: Step 1: Establishing a simplified model of the relative motion between the projectile and the target, and obtaining the relative motion relationship between the projectile and the target based on the simplified model; Step 2: Determining the guidance equation based on the relative motion relationship between the projectile and the target; Step 3: Determining the extended proportional guidance law based on the guidance equation and the landing angle constraint, thereby realizing extended proportional guidance with landing angle constraints.

[0004] A multi-vehicle cooperative terminal guidance method with line-of-sight separation angle constraint needs to be proposed. Summary of the Invention

[0005] This invention provides a multi-vehicle cooperative terminal guidance method and related products with line-of-sight separation angle constraints.

[0006] The technical solution of this invention is: a multi-vehicle cooperative terminal guidance method with line-of-sight separation angle constraint, applied to a leader aircraft in the multi-vehicle group, wherein the multi-vehicle group includes a leader aircraft and at least one follower aircraft, and the method includes:

[0007] Determine the status information of the leader vehicle, including the target distance x of the leader vehicle at the initial moment of terminal guidance. LT The flight speed V of the pilot aircraft L And the following parameters defined in the local inertial coordinate system of the pilot vehicle: line-of-sight tilt angle λ at the initial moment of terminal guidance. L0 Line-of-sight tilt velocity λ' at the initial moment of terminal guidance L0 Line-of-sight deflection η at the initial moment of terminal guidanceL0 Line-of-sight deflection angular velocity η' at the initial moment of terminal guidance L0 The x-position at time t L x L Position velocity lead angle θ L and velocity advance angle x L The angle of view θ of the position LS and line of sight angle In x L Position of the target distance R L ;

[0008] Determine the command polynomial coefficients a based on the pilot aircraft's status information and the following equation. L1 b L1 c L1 d L1 a L2 b L2 c L2 d L2 And the line-of-sight deflection η at the end of terminal guidance, defined in the local inertial coordinate system of the pilot aircraft. Lf :

[0009]

[0010]

[0011]

[0012] Where, λ Lf T is the desired line-of-sight tilt angle at the end of terminal guidance, defined in the local inertial coordinate system of the pilot vehicle. It is a preset value. go The preset expected flight time for the terminal guidance phase;

[0013] The line-of-sight tilt tracking error x of the pilot aircraft is generated based on the obtained command polynomial coefficients and the following equation. L1 Line-of-sight tilt velocity tracking error x L2 Line-of-sight tracking error x L3 Line-of-sight angular velocity tracking error x L4 The sliding surface function s related to the line-of-sight tilt tracking error L1 The sliding surface function s related to the line-of-sight angle tracking error L2 :

[0014]

[0015]

[0016]

[0017]

[0018] Where, k L0 To facilitate the calculation of the selected intermediate variables, l L1 l L2 l L3 l L4 m L1 m L2 m L3 m L4 p L1 p L2 The preset sliding surface guidance constant has a value range of l. L1 >0、l L2 >0、l L3 >0、l L4 >0、m L1 >1, 0 <m L2 <1、m L3 >1、0 <m L4 <1、p L1 >0、p L2 >0, sign m (·)=sign(·)|·| m It is a sign function with an exponent;

[0019] The normal acceleration command a for the pilot aircraft is determined according to the following equation. Ly Lateral acceleration command a Lz ;

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] Where, k L1 k L2 k L3 k L4 k L5 k L6 K Ls1 K Ls2 A L B L To simplify the auxiliary variables described by the equation, R' L ,θ' LS , The target range R of the lead aircraft is respectively L Line of sight tilt θ LS , line of sight deflection relative to x L The derivative of h L1 h L2 h L3 h L4 α L1 α L2 α L3 α L4 q L1 q L2 The preset reaching law guidance constant has a value range of h. L1 >0、h L2 >0、h L3 >0、h L4 >0、α L1 >1、0<α L2 <1、α L3 >1、0<α L4 <1、q L1 >0, q L2 >0;

[0035] According to the normal acceleration command a of the lead aircraft Ly Lateral acceleration command a Lz Control the flight state of the aircraft itself.

[0036] The technical solution of this invention is: a multi-vehicle cooperative terminal guidance method with line-of-sight separation angle constraint, applied to a slave vehicle in a multi-vehicle system, wherein the multi-vehicle system includes a leader vehicle and at least one slave vehicle, and the method includes:

[0037] Determine the status information of both the slave and leader aircraft. The slave aircraft's status information includes its flight speed V. i At the initial moment of terminal guidance, the distance x from the target to the aircraft iT And the following parameters defined in the aircraft's local inertial coordinate system: line-of-sight tilt angle λ at the initial moment of terminal guidance. i0 x-position at time t i From the aircraft in x i Position velocity lead angle θ i Speed ​​lead angle x i The angle of view θ of the position iS , line of sight deflection From the aircraft in x i Position of the target distance R i The state information of the lead vehicle includes the following parameters defined in the lead vehicle's local inertial coordinate system: the expected line-of-sight deflection η at the end of terminal guidance. Lf The desired line-of-sight tilt angle λ at the end of the final guidance phase. Lf Line-of-sight tilt angle λ at the initial moment of terminal guidance L0 Line-of-sight deflection η at the initial moment of terminal guidance L0 Line-of-sight tilt velocity λ' at the initial moment of terminal guidance L0 Line-of-sight deflection angular velocity η' at the initial moment of terminal guidance L0 The state information of the lead vehicle also includes: the line-of-sight tilt angle Θ at the initial moment of terminal guidance, defined in the global inertial coordinate system. LS0 and line of sight deflection Φ LS0 The aircraft's state information also includes: the line-of-sight tilt angle Θ at the initial moment of final guidance, defined in the global inertial coordinate system. iS0 and line of sight deflection Θ iS0 ;

[0038] The command polynomial coefficients a are determined based on the state information of the lead aircraft, the state information of the slave aircraft, and the following equation. i1 b i1 c i1 d i1 a i2 b i2 c i2 d i2 And the line-of-sight tilt velocity λ' expected at the initial moment of final guidance, defined by the aircraft in the local inertial coordinate system of the aircraft. i0 η, line of sight deflection i0 Angular velocity of line of sight η' i0 The desired line-of-sight deflection angle η at the end of the terminal guidance process. if :

[0039]

[0040]

[0041]

[0042] C θi =-sinΦ iS0 cosΦ iS0 cosΘ LS0 cosΦ LS0 +cosΘ iS0 sinΘ LS0 -sinΘ iS0 sinΦ iS0 cosΘ LS0 sinΦ LS0

[0043]

[0044] c θL =-sinΘ LS0 cosΦ LS0 cosΘ iS0 cosΦ iS0 +cosΘ LS0 sinΘ iS0 -sinΘ LS0 sinΦ LS0 cosΘ iS0 sinΦ iS0

[0045]

[0046]

[0047] Where, λ if Let c be the desired line-of-sight tilt angle at the end of terminal guidance, defined in the aircraft's local inertial coordinate system, and be a preset value. θi , c θL , To simplify the auxiliary variables described by the equation, T go The preset expected flight time for the terminal guidance phase;

[0048] The tracking error x from the aircraft's line-of-sight tilt angle is generated based on the obtained command polynomial coefficients and the following equation. i1 Line-of-sight tilt velocity tracking error x i2 Line-of-sight tracking error x i3 Line-of-sight angular velocity tracking error x i4 The sliding surface function s related to the line-of-sight tilt tracking error i1The sliding surface function s related to the line-of-sight angle tracking error i2 :

[0049]

[0050]

[0051]

[0052]

[0053] Where; k i0 To facilitate the calculation of the selected intermediate variables, l i1 l i2 l i3 l i4 m i1 m i2 m i3 m i4 p i1 p i2 The preset sliding surface guidance constant has a value range of l. i1 >0、l i2 >0、l i3 >0、l i4 >0、m i1 >1、0 <m i2 <1、m i3 >1、0 <m i4 <1、p i1 >0、p i2 >0, sign m (·)=sign(·)|·| m It is a sign function with an exponent;

[0054] The normal acceleration command a from the aircraft is determined according to the following equation. iy Lateral acceleration command a iz ;

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] Where, k i1 k i2 k i3 k i4 k i5 k i6 K is1 K is2 A i B i To simplify the auxiliary variables described by the equation, R' i ,θ' iS , The distance R from the target of the aircraft are respectively i Line of sight tilt θ iS , line of sight deflection relative to x i The derivative of h i1 h i2 h i3 h i4 α i1 α i2 α i3 α i4 q i1 q i2 The preset reaching law guidance constant has a value range of h. i1 >0、h i2 >0、h i3 >0、h i4 >0、α i1 >1、0<α i2 <1、α i3 >1、0<α i4 <1、q i1 >0, q i2 >0;

[0070] According to the normal acceleration command a from the aircraft iy Lateral acceleration command aiz Control over the aircraft's own motion state.

[0071] The technical solution of the present invention is as follows: a multi-vehicle system, including a leader aircraft and a follower aircraft, wherein the leader aircraft has a controller for executing the aforementioned multi-vehicle cooperative terminal guidance method with line-of-sight separation angle constraint applied to the leader aircraft, and the follower aircraft has a controller for executing the aforementioned multi-vehicle cooperative terminal guidance method with line-of-sight separation angle constraint applied to the leader aircraft.

[0072] The technical solution of the present invention is: a program product, characterized in that it executes the aforementioned multi-vehicle cooperative terminal guidance method with line-of-sight separation angle constraint during operation.

[0073] The technical solution of the present invention is as follows: an aircraft, including a memory and a processor, wherein a program is stored in the memory, and the program executes the aforementioned multi-aircraft cooperative terminal guidance method with line-of-sight separation angle constraint when it is run on the processor.

[0074] This invention introduces line-of-sight separation angle constraints into the design of cooperative terminal guidance laws. Addressing the shortcomings of existing research in handling line-of-sight separation angle constraints, it proposes a cooperative terminal guidance law based on a line-of-sight angle command polynomial that simultaneously controls the line-of-sight separation angle, attack time, and attack angle. This invention establishes a three-dimensional motion model coupling longitudinal and lateral channels, obtaining an analytical form of the multi-constraint terminal guidance law. Its stability can be rigorously proven theoretically, and it does not require controllable aircraft speed, thus possessing strong engineering practicality. The finite-time sliding mode guidance law employed in this invention has a faster convergence speed than the extended proportional guidance law, converging the line-of-sight angle to the desired value before target impact and reducing control command chattering. Attached Figure Description

[0075] Figure 1 For the present invention, there are two aircraft M. L M i Three-dimensional cooperative guidance geometry for a relatively stationary target T.

[0076] Figure 2 In one embodiment of the present invention, the aircraft M L M i The flight path.

[0077] Figure 3 In one embodiment of the present invention, the aircraft M L M i The curves showing the changes in the line-of-sight angle and line-of-sight separation angle over time.

[0078] Figure 4 In one embodiment of the present invention, the aircraft M L M i The curve showing the change of velocity lead angle (or lead tilt angle) over time.

[0079] Figure 5 In one embodiment of the present invention, the aircraft M L M i The hit time error curve over time.

[0080] Figure 6a and Figure 6b In one embodiment of the present invention, the aircraft M L M i The curves showing the change of acceleration commands in the y and z directions over time.

[0081] Figure 7 This is a block diagram of the controller in the aircraft of the present invention. Detailed Implementation

[0082] The present invention will be further described below with reference to specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0083] The following section presents the design concept of this method, describes its operation process, verifies the method, and provides the corresponding product.

[0084] Step 1: Based on the leader-slave cooperative guidance architecture, considering the nonlinear dynamic characteristics of the aircraft and the requirements for cooperative target localization, a description of the multi-aircraft cooperative terminal guidance problem with line-of-sight separation angle constraints is given in three-dimensional space.

[0085] Step 1.1: The research object of this problem is a multi-vehicle system (including one leader vehicle and at least one follower vehicle) in the terminal guidance phase. It uses infrared or passive radar seekers to detect target radiation signals, and achieves cooperative positioning and tracking of the target by satisfying the line-of-sight separation angle constraint among multiple vehicles through cooperative guidance. The system composed of leader and follower vehicles controls the homing maneuver based on the guidance information provided by the seeker and uses aerodynamics to correct guidance deviations. In response to the dense defense of the enemy's anti-missile system, it improves the reliability of penetration by attacking simultaneously. It uses warheads such as high-explosive fragmentation, high-explosive, and penetrating warheads to achieve efficient damage to the target at the desired attack angle.

[0086] The following assumptions are used in the problem modeling and solving process:

[0087] 1) Ignore the dynamic characteristics of the aircraft and treat it as a point mass;

[0088] 2) The target is a stationary target;

[0089] 3) The leader and follower aircraft travel at speeds V and V respectively. L V i In uniform motion, the applied acceleration vector only changes the direction of the velocity, not its magnitude.

[0090] 4) During terminal guidance, the aircraft's line-of-sight angle can be considered to vary around a specific design value, and its velocity lead angle, i.e., the angle between the velocity vector and the missile-eye line-of-sight vector, can be considered to be a small amount;

[0091] 5) Expected hit time T go Pre-designated or led by aircraft M L After the decision is made, it is transmitted to the slave aircraft M via data link. i That is, T go For each aircraft, it is a known global variable;

[0092] 6) Leading aircraft M L Independent guidance, and transmits its own guidance constants related to line-of-sight control to the slave aircraft M via data link. i From aircraft M i Cooperative terminal guidance is implemented according to anti-interference detection requirements.

[0093] Step 1.2: For the lead aircraft M L From aircraft M i The system, as a whole, has the following objectives for coordinated terminal guidance missions.

[0094] Leading aircraft M L Mission objective: its hit time T Lf =T go (T go (Indicates the expected hit time), and the line-of-sight angle θ at the moment of hit. LSf =λ Lf (λ Lf (This represents the expected line-of-sight tilt angle at the moment of impact of the guided aircraft), and the line-of-sight deflection angle at the moment of impact. (η Lf (This indicates the expected line-of-sight deflection angle when the aircraft hits the target).

[0095] The i-th from spacecraft M i Mission objective: its hit time T if =T go From the moment of hit T if Retention time T of forward co-configuration s During the period, aircraft M L M i The line-of-sight separation angle Λ Li =Ω (Ω represents the line-of-sight separation angle, which is a preset constant). Line-of-sight tilt angle θ at the moment of impact. iSf =λ if (λ if The expected trajectory inclination angle when the i-th missile hits the aircraft, and the line-of-sight deflection angle are determined by the line-of-sight separation angle constraint. The retention time T of the cooperative configuration. sThe line-of-sight separation angle Ω is a predetermined value based on the specific target positioning accuracy requirements.

[0096] Step 1.3: Establish the leader aircraft M L From aircraft M i The three-dimensional relative motion relationship between them is as follows: Figure 1 As shown, Oxyz is the global inertial coordinate system, T represents a stationary target, and R... L R i θ represents the missile-target distance between the lead aircraft and the follower aircraft, respectively. L θ i These are the pitch lead angle (velocity lead angle) of the lead aircraft and the follower aircraft relative to the line of sight. These are the yaw angles (velocity yaw angles) of the lead aircraft and the follower aircraft relative to the line of sight, θ. LS θ iS These are the tilt angles of view for the lead aircraft and the aircraft from its line of sight. These are the line-of-sight angles of the lead aircraft and the follower aircraft, respectively. The velocity vector of the lead aircraft is denoted as V. L The i-th from spacecraft M i The velocity vector is denoted as V i .

[0097] Leading aircraft M L From aircraft M i The equations of relative motion between the projectile and the target, with time t as the independent variable, are as follows:

[0098]

[0099]

[0100] a yL For the normal acceleration command of the leading aircraft to be solved, a zL Let a be the lateral acceleration command of the leading aircraft to be solved. yi For the normal acceleration command from aircraft i to be solved, a zi The lateral acceleration command from aircraft i is to be solved.

[0101] The black dot above the symbol indicates the derivative with respect to time. The aircraft controls its motion based on the obtained normal acceleration and lateral acceleration commands.

[0102] Step 1.4: To facilitate the establishment of constraints regarding the line-of-sight separation angle and hit time, the above equations of relative motion between the projectile and the target are rewritten as shown in equation (3), with the horizontal coordinate x as the independent variable. Equation (3) does not distinguish between the lead and follower aircraft.

[0103]

[0104]

[0105]

[0106]

[0107] Where t is the flight time, and V represents the flight speed of the leading aircraft. L Or from the flight speed V of aircraft i i θ S The line-of-sight tilt angle θ of the pilot aircraft is indicated. LS Or the tilt angle θ from the line of sight of aircraft i iS , Indicates the line-of-sight deflection angle of the pilot aircraft. Or from the line of sight angle of aircraft i θ represents the velocity lead angle of the pilot aircraft. L Or from the velocity of aircraft i, the forward tilt angle θ i , Indicates the leading angle of the aircraft's velocity. Or from the velocity advance angle of aircraft i R represents the target distance of the aircraft. L Or from the target distance R of aircraft i i a y The command 'a' indicates the normal acceleration of the pilot aircraft. Ly Or from the normal acceleration command a of aircraft i iy a z The command a represents the lateral acceleration of the pilot aircraft. Lz Or from the lateral acceleration command a of aircraft i iz For ease of discussion, k0, k1, and k2 are chosen as auxiliary parameters to simplify the equation description. They are functions of state variables such as line-of-sight tilt angle, line-of-sight deflection angle, velocity lead angle, and velocity lead deflection angle. The symbol ' indicates differentiation with respect to the x-axis.

[0108] Step 1.5: Line of sight tilt velocity θ′ S Line of sight tilt velocity Taking the derivative with respect to the x-coordinate, we get θ″. S and See formulas (7) to (12).

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] For ease of discussion, k3, k4, k5, and k6 are selected as auxiliary parameters to simplify the equation description.

[0116] Step 1.6: For the lead aircraft M L From aircraft M i Define local inertial coordinate systems F respectively IL F Ii .

[0117] Local inertial coordinate system F IL The origin of the coordinate system is the position of the lead vehicle at the initial moment of the terminal guidance phase. The directions of each coordinate axis are the same as the missile-target line-of-sight coordinate system of the lead vehicle at that moment. That is, the x-axis points to the target along the missile-target line-of-sight of the lead vehicle, the y-axis is perpendicular to the x-axis and goes upward in the vertical plane, and the z-axis forms a right-hand rectangular coordinate system with the x-axis and y-axis.

[0118] Local inertial coordinate system F Ii The origin of the coordinate system is the position of the aircraft at the initial moment of the final guidance phase. The directions of each coordinate axis are the same as the missile-eye line-of-sight coordinate system at that moment. That is, the x-axis points to the target along the missile-eye line-of-sight of the aircraft, the y-axis is perpendicular to the x-axis and goes upward in the vertical plane, and the z-axis forms a right-hand rectangular coordinate system with the x-axis and y-axis.

[0119] θ LS0 The elevation angle of the missile's line-of-sight vector relative to the xoz plane of the global inertial coordinate system at the initial moment of terminal guidance, Ф LS0 θ is the angle between the projection of the missile-target line-of-sight vector of the lead vehicle onto the xoz plane of the global inertial coordinate system at the initial moment of terminal guidance and the x-axis. iS0 Let Ф be the elevation angle of the aircraft's line-of-sight vector relative to the xoz plane of the global inertial coordinate system at the initial moment. iS0 The angle between the projection of the missile's line-of-sight vector from the aircraft onto the xoz plane of the global inertial coordinate system at the initial moment and the x-axis.

[0120] In the local inertial coordinate system F IL F Ii The M-class aircraft is defined separately. L From aircraft M i Given the line-of-sight angle and velocity lead angle, it is easy to see that the equations of relative motion between the projectile and the target have the same form. Furthermore, during the terminal guidance process, the line-of-sight tilt angle, line-of-sight deflection angle, velocity lead angle (referred to as lead angle), and lead deflection angle (referred to as lead angle) can be considered as small quantities.

[0121] The line-of-sight tilt angle, line-of-sight deflection angle, velocity lead angle, and velocity lead deflection angle in the local inertial coordinate system are denoted as θ. S , and θ, The line-of-sight tilt angle, line-of-sight deflection angle, velocity lead angle, and velocity lead deflection angle in the global inertial coordinate system are denoted as θ. S Ф S And θ, Ф.

[0122] Step 2: In the local inertial coordinate system F I (No distinction is made between lead and follow aircraft) In this process, command polynomials for the missile-target line-of-sight angle and line-of-sight angular velocity are constructed, and the polynomial coefficients are solved using boundary conditions.

[0123] Step 2.1: For both the lead and follower aircraft, construct command polynomials for the desired line-of-sight angle and line-of-sight angular velocity in the following forms:

[0124]

[0125] In the formula x T Let θ be the x-axis position of the target point in the local inertial coordinate system. Sd , The expected line-of-sight tilt angle and line-of-sight deflection angle are respectively represented by cubic polynomials. a1, b1, c1, and d1 are the undetermined coefficients of the line-of-sight tilt angle polynomial (intermediate variables that need to be solved during the operation of the lead aircraft and transmitted to the follow aircraft), and a2, b2, c2, and d2 are the undetermined coefficients of the line-of-sight deflection angle polynomial (intermediate variables that need to be solved during the operation of the lead aircraft and transmitted to the follow aircraft). These are the corresponding line-of-sight tilt rate and line-of-sight deflection rate, respectively, from The derivative with respect to the variable x is obtained.

[0126] Step 2.2: In the local inertial coordinate system, the spacecraft is initially located at the origin, therefore x0 = 0, θ S0 =0、 At the same time, the direction of the aircraft's velocity should coincide with the line of sight of the target at the moment of impact, that is, the line-of-sight angular rate should be zero, θ′ Sdf =0,

[0127] x0 is the x-direction displacement at the initial moment of final guidance, θ S0 The line-of-sight tilt angle at the initial moment of terminal guidance. The line-of-sight deflection angle at the initial moment of terminal guidance, θ′ Sdf It is the rate of the line of sight tilt at the moment of impact. It is the rate of line-of-sight deflection at the moment of impact.

[0128] Let the desired initial line-of-sight tilt angle be θ Sd0 =λ0, the desired initial line-of-sight tilt velocity θ′ Sd0 =λ0′, the desired terminal line-of-sight tilt angle θ Sdf =λ f ; Expected initial line-of-sight deflection Desired initial line-of-sight deflection velocity Desired terminal line of sight deflection

[0129] Substituting the above boundary conditions into equations (13) to (16), we get:

[0130]

[0131]

[0132] Step 2.3: Solve the above two systems of four linear equations to obtain the following solution with undetermined polynomial coefficients:

[0133]

[0134]

[0135] Step 3: Under the condition that the aircraft flies according to the desired line-of-sight angle and line-of-sight angular velocity variation law, obtain the relationship between the remaining flight time and the coefficients of the command polynomial.

[0136] Step 3.1: The remaining flight time during the terminal guidance process can be predicted based on the command polynomial by the following integral:

[0137]

[0138] T go It is the remaining flight time during the final guidance process.

[0139] Step 3.2: Considering the line-of-sight tilt angle θ S , line of sight deflection Pre-velocity tilt angle θ, Pre-velocity deflection angle For small quantities, performing a Taylor expansion on the trigonometric functions in equation (21) and ignoring small quantities of order three and above, the above equation can be approximated as:

[0140]

[0141] Step 3.3: When the aircraft flies according to the desired line-of-sight angle and line-of-sight angular velocity variation patterns, the following relationship holds:

[0142]

[0143] Step 3.4: Perform Taylor expansion on equations 3 and 4 in equation (23), and ignore third-order and higher-order small quantities to obtain an approximate expression for the velocity lead angle:

[0144]

[0145] Step 3.5: Substitute equations (23) and (24) into equation (22) to obtain the relationship between the remaining flight time and the coefficients of the command polynomial:

[0146]

[0147] Step 4: Derive the relationship between the line-of-sight separation angle and the command polynomial coefficients of the lead and follower aircraft in the global inertial coordinate system.

[0148] Figure 1 M L TM i The angle is the line-of-sight separation angle.

[0149] Step 4.1: Aircraft M L M i The transformation relationship between the local inertial coordinate system and the global inertial coordinate system is given by θ. LS0 Ф LS0 θ iS0 Ф iS0 Sure.

[0150] At time t, spacecraft M L M i The line-of-sight vectors in the global inertial coordinate system can be expressed as:

[0151]

[0152]

[0153] For the lead aircraft M L The line-of-sight vector. For the aircraft M i The line-of-sight vector.

[0154] Step 4.2: Aircraft M L M i line-of-sight separation angle Λ Li for:

[0155]

[0156] Considering θ LS , θ iS , For a small quantity, the following was obtained:

[0157]

[0158]

[0159]

[0160]

[0161]

[0162]

[0163] For ease of discussion, we choose c. θL , c θi , C is an auxiliary parameter.

[0164] Step 4.3: Considering the small change in line-of-sight velocity during terminal guidance, under the condition of simultaneous hits, it is easy to know that:

[0165]

[0166] x i (t) is the x-direction displacement of the spacecraft in the local inertial coordinate system at time t, where x L (t) is the x-direction displacement of the pilot spacecraft in the local inertial coordinate system at time t, x Ti It is the target's x-coordinate in the local inertial coordinate system of the aircraft, x TL It is the x-coordinate of the target in the local inertial coordinate system of the pilot aircraft.

[0167] For ease of discussion, select Auxiliary parameters, λ i0 , λ if These are the line-of-sight tilt angles from the initial moment and the moment of impact of the aircraft, respectively, η i0 η if These are the line-of-sight angles from the initial moment of the aircraft and the moment of impact, respectively; λ L0 , λ Lf These are the line-of-sight tilt angles of the lead aircraft at the initial moment and the moment of impact, respectively, η L0 η Lf These are the initial moment of the pilot's flight and the line-of-sight angle at the moment of impact.

[0168] For different orders of x, we write out the equations respectively, and obtain the following about the parameter. λ i0 , λ if , η i0η if , λ L0 , λ Lf , η L0 η Lf The system of linear equations:

[0169]

[0170] Step 4.4: The rank of the characteristic matrix of the above system of equations is 3. When C = 0, the system of equations has a solution. Under this condition, consider... λ L0 , λ Lf , η L0 η Lf , λ i0 , λ if Given quantities, it is easy to find:

[0171]

[0172] In the local inertial coordinate systems of the lead vehicle (labeled as the lead missile in the attached diagram) and the follower vehicle (labeled as the follower missile in the attached diagram), the desired line-of-sight angle and line-of-sight angular velocity variation laws are defined. The command polynomial is uniquely determined by the parameters of initial line-of-sight tilt angle, initial line-of-sight tilt velocity, terminal line-of-sight tilt angle, initial line-of-sight deflection angle, initial line-of-sight deflection velocity, and terminal line-of-sight deflection angle. Among these parameters, all parameters involving the lead missile and the initial and terminal line-of-sight tilt angles of the follower missile are generated freely, while the other parameters of the follower missile are obtained based on the remaining flight time and line-of-sight separation angle constraints. Except for the solution process of the command polynomial, the guidance law design processes for the lead and follower missiles are the same.

[0173] Step 5: Based on the above command polynomials for line-of-sight angle and line-of-sight angular velocity, and their constraints with the remaining flight time and line-of-sight separation angle, the terminal guidance law is designed using the finite-time sliding mode guidance method.

[0174] Step 5.1: Select the line-of-sight angle and line-of-sight angular velocity tracking deviation as state variables:

[0175]

[0176] Step 5.2: To achieve rapid tracking of the desired line-of-sight angle and line-of-sight angular velocity, fast double-power-law approaching sliding surfaces are designed for both the pitch and yaw channels:

[0177]

[0178]

[0179]

[0180]

[0181] In the formula, s1 is the sliding surface function of the pitch channel, s2 is the sliding surface function of the yaw channel, and sign m (·)=sign(·)|·| m It is a sign function with an exponent.

[0182] l1, l2, l3, l4, m1, m2, m3, m4, p1, p2 are preset constant guidance gains (sliding surface guidance constants) related to the sliding mode structure; h1, h2, h3, h4, α1, α2, α3, α4, q1, q2 are preset constant guidance gains (reaching law guidance constants) related to the reaching law, with values ​​ranging from: l1>0, l2>0, p1>0, m1>1, 0. <m2<1,l3> 0, l4>0, p2>0, m3>1, 0 <m4<1,h1> 0, h2>0, q1>0, α1>1, 0<α2<1, h3>0, h4>0, q2>0, α3>1, 0<α4<1.

[0183] Step 5.3: Differentiate the above sliding surface function with respect to the x-coordinate to obtain:

[0184]

[0185]

[0186] Step 5.4: Combining equations (7), (8), and (38), we obtain:

[0187]

[0188]

[0189]

[0190]

[0191] In the formula, K s1 K s2 These are auxiliary parameters independent of acceleration commands, used to simplify the equation description.

[0192] Step 5.5: Combining equations (41), (42), (45), and (47), we obtain the guidance law in analytical form as follows:

[0193]

[0194]

[0195]

[0196] Here, A and B are auxiliary parameters that simplify the equation description.

[0197] Based on the above design concept, a multi-aircraft cooperative terminal guidance method with line-of-sight separation angle constraints can be obtained. The execution entity can be the aircraft controller or a program running on the controller. This invention does not limit the hardware form of the controller, such as memory and processor, programmable logic device (FPGA), or application-specific integrated circuit (ASIC).

[0198] The operation process of the pilot aircraft is as follows.

[0199] Determine the coefficients a of the instruction polynomial according to the following equation. L1 b L1 c L1 d L1 a L2 b L2 c L2 d L2 And the line-of-sight deflection η at the end of terminal guidance, defined in the local inertial coordinate system of the pilot aircraft. Lf :

[0200]

[0201]

[0202]

[0203] Where, λ L0 Let λ' be the line-of-sight tilt angle defined in the local inertial coordinate system of the pilot vehicle at the initial moment of terminal guidance. L0 Let η be the line-of-sight tilt velocity at the initial moment of terminal guidance, defined in the local inertial coordinate system of the pilot vehicle. L0 Let η' be the line-of-sight deflection angle at the initial moment of terminal guidance, defined in the local inertial coordinate system of the pilot vehicle. L0 The line-of-sight deflection angular velocity at the initial moment of terminal guidance, defined in the local inertial coordinate system of the pilot vehicle, is obtained through sensor detection; λ Lf The line-of-sight tilt angle, defined in the local inertial coordinate system of the lead vehicle, at the desired moment of termination of terminal guidance, is preset according to the damage performance requirements; V L The flight speed of the aircraft is calculated by the flight controller using navigation; x LTThe target-missile distance of the lead vehicle at the initial moment of final guidance is obtained using the sine theorem within the detection triangle formed by the lead and follow vehicles and the target. The required known parameters include the lead vehicle's initial x-axis position x in the global inertial coordinate system. L0 y-position L0 z-position L0 Line of sight angle Θ LS0 Φ (Line of sight deflection) LS0 In the global inertial coordinate system, the coordinates from the initial x-axis of the spacecraft to its position x-axis are defined. i0 y-position i0 z-position i0 Angle of view Θ iS0 Φ (Line of sight deflection) iS0 The parameters of the leader aircraft are obtained through navigation calculations by the controller and detection by the detectors, while the parameters of the slave aircraft are obtained through communication between the leader and slave aircraft; T go This parameter represents the expected flight time during the terminal guidance phase. It is the same for both the lead and follower aircraft and is preset according to the requirements of the cooperative terminal guidance mission.

[0204] Based on the obtained command polynomial coefficients, the line-of-sight tilt tracking error x of the pilot aircraft is generated according to the following equation. L1 Line-of-sight tilt velocity tracking error x L2 Line-of-sight tracking error x L3 Line-of-sight angular velocity tracking error x L4 The sliding surface function s related to the line-of-sight tilt tracking error L1 The sliding surface function s related to the line-of-sight angle tracking error L2 :

[0205]

[0206]

[0207]

[0208]

[0209] Where, x L Let θ be the x-position at time t defined in the local inertial coordinate system of the pilot aircraft, replacing t as the independent variable of the system; L , The leading aircraft in x L The position's velocity lead angle and lead angle are obtained through navigation via the flight controller; θ LS , x, defined in the local inertial coordinate system of the pilot aircraft, are respectively LThe line-of-sight tilt angle and line-of-sight deflection angle at the location are obtained through sensor detection; R L To lead the aircraft in x L The target-missile distance is determined using the sine theorem within the detection triangle formed by the lead and follower aircraft and the target. The required known parameters include the lead aircraft's x-axis position at time t, as defined in the global inertial coordinate system. L y-position L z-position L Line of sight angle Θ LS Φ (Line of sight deflection) LS The x-axis position of the spacecraft at time t, defined in the global inertial coordinate system. i y-position i z-position i Angle of view Θ iS Φ (Line of sight deflection) iS The parameters of the leader aircraft are obtained through navigation calculations by the controller and detection by the detectors, while the parameters of the slave aircraft are obtained through communication between the leader and slave aircraft; k L0 The intermediate variable selected for ease of calculation is the line-of-sight tilt angle θ of the pilot aircraft. LS , line of sight deflection Pre-velocity tilt angle θ L Forward deflection angle The function; l L1 l L2 l L3 l L4 m L1 m L2 m L3 m L4 p L1 p L2 The guiding constant for the pre-designed sliding surface has a value range of l. L1 >0、l L2 >0、l L3 >0、l L4 >0、m L1 >1、0 <m L2 <1、m L3 >1、0 <m L4 <1、p L1 >0、p L2 >0.

[0210] The normal acceleration command a for the pilot aircraft is determined according to the following equation. Ly Lateral acceleration command a Lz ;

[0211]

[0212]

[0213]

[0214]

[0215]

[0216]

[0217]

[0218]

[0219]

[0220]

[0221]

[0222]

[0223]

[0224]

[0225] Where, k L1 k L2 k L3 k L4 k L5 k L6 K Ls1 K Ls2 A L B L Auxiliary variables to simplify the equation description; R' L ,θ' LS , The target range R of the lead aircraft is respectively L Line of sight tilt θ LS , line of sight deflection relative to x L The derivative of h; L1 h L2 h L3 h L4 α L1 α L2 α L3 α L4 q L1 q L2 The pre-designed approach law guidance constant takes values ​​in the range of h. L1 >0、h L2 >0、h L3>0、h L4 >0、α L1 >1、0<α L2 <1、α L3 >1、0<α L4 <1、q L1 >0, q L2 >0.

[0226] According to the normal acceleration command a of the lead aircraft Ly Lateral acceleration command a Lz Control the flight state of the aircraft itself.

[0227] Specifically, according to the normal acceleration command a of the pilot aircraft Ly Lateral acceleration command a Lz The flight controller calculates the actuation commands of the servo mechanism, controls the change in the attitude of the aircraft, generates the required acceleration commands, and achieves the desired multi-constraint terminal guidance.

[0228] The target range of the lead aircraft x LT At the initial moment of final guidance, the law of sine is applied to the detection triangle formed by the leader and follower aircraft and the target. The following equation is used to obtain the position of the leader aircraft in the x-direction at the initial moment, as defined in the global inertial coordinate system. L0 y-position L0 z-position Z L0 Line of sight angle Θ LS0 Φ (Line of sight deflection) LS0 In the global inertial coordinate system, the coordinates from the initial x-axis of the spacecraft to its position X-axis are defined. i0 y-position i0 z-position Z i0 Angle of view Θ iS0 Φ (Line of sight deflection) iS0 The parameters of the leader aircraft are obtained through navigation calculations by the controller and detection by the detectors, while the parameters of the slave aircraft are obtained through communication between the leader and slave aircraft.

[0229]

[0230]

[0231]

[0232] Λ LTi0 =cos -1 (cosΘ LS0 cosΘ iS0 cos(Φ LS0 -Φ iS0 )+sinΘ LS0 sinΘiS0 )

[0233] Λ TiL0 =cos -1 (cosΘ iL0 cosΘ iS0 cos(Θ iL0 -Θ iS0 )+sinΘ iL0 sinΘ iS0 )

[0234]

[0235] R iL0 Θ iL0 Φ iL0 Λ LTi0 Λ TiL0 It is an intermediate variable.

[0236] Among them, the target range R of the lead aircraft L At time t, using the law of sine in the detection triangle formed by the leader, follower, and target, the following equation is obtained. The known parameters required include the leader's x-axis position X at time t, as defined in the global inertial coordinate system. L y-position L z-position Z L Line of sight angle Θ LS Φ (Line of sight deflection) LS In the global inertial coordinate system, the coordinates from the initial x-axis of the spacecraft to its position X-axis are defined. i y-position i z-position Z i Angle of view Θ iS Φ (Line of sight deflection) iS The parameters of the leader aircraft are obtained through navigation calculations by the controller and detection by the detectors, while the parameters of the slave aircraft are obtained through communication between the leader and slave aircraft.

[0237]

[0238]

[0239]

[0240] Λ LTi =cos -1 (cosΘ LS cosΘ iS cos(Θ LS -Φ iS )+sinΘ LS sinΘ iS )

[0241] Λ TiL =cos -1 (cosΘ iL cosΘ iS cos(Φ iL -Φ iS )+sinΘ iL sinΘ iS )

[0242]

[0243] R iL Θ iL Φ iL Λ LTi Λ TiL It is an intermediate variable.

[0244] In this way, the target distance of the guided aircraft can be more accurate.

[0245] The operation process of the aircraft is as follows.

[0246] Determine the coefficients a of the instruction polynomial according to the following equation. i1 b i1 c i1 d i1 a i2 b i2 c i2 d i2 And the line-of-sight tilt velocity λ' expected at the initial moment of terminal guidance, defined in the local inertial coordinate system of the aircraft. i0 η, line of sight deflection i0 Angular velocity of line of sight η' i0 The desired line-of-sight deflection angle η at the end of the terminal guidance process. if :

[0247]

[0248]

[0249]

[0250] c θi =-sinΘ iS0 cosΦ iS0 cosΘ LS0 cosΦ LS0 +cosΘ iS0 sinΘ LS0 -sinΘ iS0 sinΘ iS0 cosΘ LS0 sinΦ LS0

[0251]

[0252] c θL =-sinΘ LS0 cosΦ LS0 cosΘ iS0 cosΦ iS0 +cosΘ LS0 sinΘ iS0 -sinΘ LS0 sinΘ LS0 cosΘ iS0 sinΦ iS0

[0253]

[0254]

[0255] The known parameters are as follows: λ i0 The line-of-sight tilt angle, defined in the local inertial coordinate system of the aircraft at the initial moment of terminal guidance, is obtained through sensor detection; λ if The line-of-sight tilt angle, defined in the local inertial coordinate system of the aircraft, at the desired moment of termination of terminal guidance, is preset according to the damage performance requirements; V i The speed is calculated from the aircraft's flight speed using navigation techniques from the flight controller; x iT The distance between the missile and the target at the initial moment of final guidance is obtained using the law of sine in the detection triangle formed by the leader, follower, and target aircraft. The required known parameters include the initial x-axis position of the leader aircraft in the global inertial coordinate system. L0 y-position L0 z-position L0 Line of sight angle Θ LS0 Φ (Line of sight deflection) LS0 In the global inertial coordinate system, the coordinates from the initial x-axis of the spacecraft to its position x-axis are defined. i0 y-position i0 z-position i0 Angle of view Θ iS0 Φ (Line of sight deflection) iS0 The parameters of the lead aircraft are obtained through navigation calculations by the controller and detection by the detectors; the parameters of the leader aircraft are obtained through communication between the leader and follower aircraft. θi , c θL , Auxiliary variables used to simplify the description of the equation.

[0256] The last seven equations above reflect the constraints on the line-of-sight separation angle.

[0257] The known parameters of the leader aircraft also include: the leader aircraft's state information, which includes the following parameters defined in the leader aircraft's local inertial coordinate system: the expected line-of-sight deflection η at the end of terminal guidance. Lf The desired line-of-sight tilt angle λ at the end of the final guidance phase. Lf Line-of-sight tilt angle λ at the initial moment of terminal guidance L0 Line-of-sight deflection η at the initial moment of terminal guidance L0 Line-of-sight tilt velocity λ' at the initial moment of terminal guidance L0 Line-of-sight deflection angular velocity η' at the initial moment of terminal guidance L0 .

[0258] Based on the obtained command polynomial coefficients, the line-of-sight tilt tracking error x from the aircraft is generated according to the following equation. i1 Line-of-sight tilt velocity tracking error x i2 Line-of-sight tracking error x i3 Line-of-sight angular velocity tracking error x i4 The sliding surface function s related to the line-of-sight tilt tracking error i1 The sliding surface function s related to the line-of-sight angle tracking error i2 :

[0259]

[0260]

[0261]

[0262]

[0263] Where, x i Let θ be the x-position at time t, defined in the local inertial coordinate system of the aircraft, replacing t as the independent variable of the system; i , From the spacecraft at x i The position's velocity lead angle and lead angle are obtained through navigation via the flight controller; θ iS , x, defined in the local inertial coordinate system of the aircraft, are respectively i The line-of-sight tilt angle and line-of-sight deflection angle at the location are obtained through sensor detection; R i For the aircraft in x i The target-missile distance is determined using the sine theorem within the detection triangle formed by the lead and follower aircraft and the target. The required known parameters include the lead aircraft's x-axis position at time t, as defined in the global inertial coordinate system. L y-position L z-position L Line of sight angle Θ LSΦ (Line of sight deflection) LS The x-axis position of the spacecraft at time t, defined in the global inertial coordinate system. i y-position i z-position i Angle of view Θ iS Φ (Line of sight deflection) iS The parameters of the lead aircraft are obtained through navigation calculations by the controller and detection by the detectors; the parameters of the leader aircraft are obtained through communication between the leader and follower aircraft. i0 The intermediate variable selected for ease of calculation is the tilt angle θ of the aircraft's line of sight. iS , line of sight deflection Pre-velocity tilt angle θ i Forward deflection angle The function; l i1 l i2 l i3 l i4 m i1 m i2 m i3 m i4 p i1 p i2 The guiding constant for the pre-designed sliding surface has a value range of l. i1 >0、l i2 >0、l i3 >0、l i4 >0、m i1 >1、0 <m i2 <1、m i3 >1、0 <m i4 <1、p i1 >0、p i2 >0.

[0264] The normal acceleration command a from the aircraft is determined according to the following equation. iy Lateral acceleration command a iz ;

[0265]

[0266]

[0267]

[0268]

[0269]

[0270]

[0271]

[0272]

[0273]

[0274]

[0275]

[0276]

[0277]

[0278]

[0279] Where, k i1 k i2 k i3 k i4 k i5 k i6 K is1 K is2 A i B i Auxiliary variables to simplify the equation description; R' i ,θ' iS , The distance R from the target of the aircraft are respectively i Line of sight tilt θ iS , line of sight deflection relative to x i The derivative of h; i1 h i2 h i3 h i4 α i1 α i2 α i3 α i4 q i1 q i2 The pre-designed approach law guidance constant takes values ​​in the range of h. i1 >0、h i2 >0、h i3 >0、h i4 >0、α i1 >1、0<α i2 <1、α i3 >1、0<α i4 <1、q i1 >0, q i2 >0.

[0280] According to the normal acceleration command a from the aircraft iy Lateral acceleration command aiz Control over the aircraft's own motion state.

[0281] Specifically, according to the normal acceleration command a from the aircraft iy Lateral acceleration command a iz The flight controller calculates the actuation commands of the servo mechanism, controls the change in the attitude of the aircraft, generates the required acceleration commands, and achieves the desired multi-constraint terminal guidance.

[0282] Among them, the target distance x of the aircraft iT At the initial moment of final guidance, the law of sine is applied to the detection triangle formed by the leader and follower aircraft and the target. The following equation is used to obtain the position of the leader aircraft in the x-direction at the initial moment, as defined in the global inertial coordinate system. L0 y-position L0 z-position Z L0 Line of sight angle Θ LS0 Φ (Line of sight deflection) LS0 In the global inertial coordinate system, the coordinates from the initial x-axis of the spacecraft to its position X-axis are defined. i0 y-position i0 z-position Z i0 Angle of view Θ iS0 Φ (Line of sight deflection) iS0 The parameters of the slave aircraft are obtained through navigation calculations by the controller and detection by the detectors, while the parameters of the leader aircraft are obtained through communication between the leader and slave aircraft.

[0283]

[0284]

[0285]

[0286] Λ LTi0 =cos -1 (cosΘ LS0 cosΘ iS0 cos(Φ LS0 -Φ iS0 )+sinΘ LS0 sinΘ iS0 )

[0287] Λ TLi0 =cos -1 (cosΘ LS0 cosΘ Li0 cos(Φ LS0 -Φ LS0 )+sinΘ LS0 sinΘ Li0 )

[0288]

[0289] R Li0 Θ Li0 Φ Li0 Λ LTi0 Λ TLi0 It is an intermediate variable.

[0290] Among them, the target distance R of the aircraft i At time t, using the law of sine in the detection triangle formed by the leader, follower, and target, the following equation is obtained. The known parameters required include the leader's x-axis position X at time t, as defined in the global inertial coordinate system. L y-position L z-position Z L Line of sight angle Θ LS Φ (Line of sight deflection) LS In the global inertial coordinate system, the coordinates from the initial x-axis of the spacecraft to its position X-axis are defined. i y-position i z-position Z i Angle of view Θ iS Φ (Line of sight deflection) iS The parameters of the slave aircraft are obtained through navigation calculations by the controller and detection by the detectors, while the parameters of the leader aircraft are obtained through communication between the leader and slave aircraft.

[0291]

[0292]

[0293]

[0294] Λ LTi =cos -1 (cosΘ LS cosΘ iS cos(Φ LS -Φ iS )+sinΘ LS sinΘ iS )

[0295] Λ TLi =cos -1 (cosΘ LS cosΘ Li cos(Φ LS -Φ Li )+sinΘ LS sinΘ Li )

[0296]

[0297] R Li Θ Li Φ Li Λ LTi Λ TLi It is an intermediate variable.

[0298] In this way, the distance between the aircraft and the target can be more accurately determined.

[0299] It should be noted that the design framework of the leader aircraft and the follower aircraft is the same. The difference is that the leader aircraft does not need to consider the line-of-sight separation angle constraint, which is implemented at the follower aircraft end.

[0300] To make the objectives, content, and advantages of this invention clearer, a simulation scenario is set up in which two aircraft cooperate to strike a stationary ground target, such as... Figure 1 The specific embodiments of the present invention are further described in detail below. The position of the stationary target is defined as (0m, 0m, 0m). The initial states of the two aircraft are shown in Table 1, and the line-of-sight polynomial boundary conditions are shown in Table 2. The desired line-of-sight angle and line-of-sight angular velocity variation laws are defined in the local inertial coordinate systems of the leader and follower aircraft. The command polynomial is uniquely determined by parameters such as the initial line-of-sight tilt angle, initial line-of-sight tilt velocity, terminal line-of-sight tilt angle, initial line-of-sight deflection angle, initial line-of-sight deflection velocity, and terminal line-of-sight deflection angle. All parameters of the leader aircraft and some parameters of the follower aircraft, such as the initial line-of-sight tilt angle and terminal line-of-sight tilt angle, are freely designed. Other parameters of the follower aircraft are obtained based on the remaining flight time and line-of-sight separation angle constraints.

[0301] Table 1. Initial Simulation Conditions for the Aircraft (Global Inertial Coordinate System)

[0302]

[0303] Table 2. Command polynomial for the aircraft's line-of-sight angle (local inertial coordinate system)

[0304]

[0305]

[0306] With the initial moment of terminal guidance as zero seconds, the expected hit time T d We take 89.44s, and the desired line-of-sight separation is 50°. We select the same sliding mode guidance constant for both the lead and follower aircraft.

[0307] l1=0.001, l2=5, m1=1.03, m2=0.15, p1=0.001;

[0308] l3=0.001, l4=5, m3=1.03, m4=0.15, p2=0.001;

[0309] h1=0.3, h2=200, α1=1.2, α2=0.95, q1=0.3;

[0310] h3=0.3, h4=200, α3=1.2, α4=0.95, q2=0.3.

[0311] Under the aforementioned initial conditions and guidance law design, a simulation was conducted where a lead aircraft and a follower aircraft jointly attacked a stationary ground target. During the simulation, the amplitude of the normal and lateral accelerations was limited to 100 m / s². 2 The obtained data includes the flight path of the lead aircraft, the line-of-sight angle, the velocity lead angle, the hit time error, and the acceleration command attachment. Figures 2 to 6b As shown in the simulation results, the line-of-sight angles of the lead and follower aircraft converge to the pre-designed command polynomial within 25 seconds, and the hit time deviation eventually converges to zero. Throughout the entire terminal guidance process, the line-of-sight separation angle remains at around 50°, verifying the feasibility of using the guidance law for cooperative guidance.

[0312] Based on the same inventive concept, embodiments of the present invention also provide a multi-vehicle system, including a leader vehicle and a follower vehicle, wherein the leader vehicle has a controller for executing the aforementioned multi-vehicle cooperative terminal guidance method with line-of-sight separation angle constraint applied to the leader vehicle, and the follower vehicle has a controller for executing the aforementioned multi-vehicle cooperative terminal guidance method with line-of-sight separation angle constraint applied to the leader vehicle.

[0313] Based on the same inventive concept, embodiments of the present invention also provide a program product, characterized in that it executes the aforementioned multi-vehicle cooperative terminal guidance method with line-of-sight separation angle constraints during runtime.

[0314] Based on the same inventive concept, and referring to Figure 7 Embodiments of the present invention also provide an aircraft, including a memory and a processor, wherein a program is stored in the memory, and the program executes the aforementioned multi-aircraft cooperative terminal guidance method with line-of-sight separation angle constraints when it is run on the processor.

[0315] The various embodiments in this invention are described in a progressive manner. For the same or similar parts between the various embodiments, please refer to each other. Each embodiment focuses on describing the differences from other embodiments.

[0316] The scope of protection of this invention is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its scope and spirit. If these modifications and variations fall within the scope of the claims of this invention and their equivalents, then the intent of this invention also includes these modifications and variations.

Claims

1. A method of multi-air vehicle cooperative terminal guidance with a line-of-sight separation angle constraint, applied to a lead air vehicle of the multi-air vehicles, wherein, The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: determining state information of the leading aircraft, the state information of the leading aircraft including a missile-target distance x of the leading aircraft at an initial time of terminal guidance LT , a flight speed V of the leading aircraft L , and the following parameters defined in a local inertial coordinate system of the leading aircraft: a line-of-sight inclination angle λ at the initial time of terminal guidance L0 , a line-of-sight inclination angle velocity λ' at the initial time of terminal guidance L0 , a line-of-sight deflection angle η at the initial time of terminal guidance L0 , a line-of-sight deflection angle velocity η' at the initial time of terminal guidance L0 , an x-direction position x at the time t L , an x L direction velocity pre-inclination angle θ L and a velocity pre-deflection angle x L direction line-of-sight inclination angle θ LS and line-of-sight deflection angle at the x L direction position L ; The command polynomial coefficients a, b, c, d, and the desired line-of-sight angle η at the end of terminal guidance defined in the local inertial frame of the lead vehicle are determined from the state information of the lead vehicle and the following equations L1 L1 L1 L1 L2 L2 L2 L2 Lf ​​​​​​​​​ where λ Lf is the desired line-of-sight angle of attack at the end of terminal guidance defined in the local inertial coordinate system of the leading aircraft, which is a preset value, T go is the desired flight time in the terminal guidance phase, which is a preset value. The line-of-sight angle tracking error x L1 , the line-of-sight angle velocity tracking error x L2 , the line-of-sight angle tracking error x L3 , the line-of-sight angle velocity tracking error x L4 , the line-of-sight angle tracking error x L1 , the line-of-sight angle velocity tracking error x L2 : where k L0 is a preset constant, l L1 is a preset constant, l L2 is a preset constant, l L3 is a preset constant, l L4 is a preset constant, m L1 is a preset constant, m L2 is a preset constant, m L3 is a preset constant, m L4 is a preset constant, p L1 is a preset constant, p L2 is a preset constant, l L1 > 0, l L2 > 0, l L3 > 0, l L4 > 0, m L1 > 1, 0 < m L2 < 1, m L3 > 1, 0 < m L4 < 1, p L1 > 0, p L2 > 0, sign m (·) = sign(·) |·| m is a sign function with an index. The normal acceleration command a of the lead aircraft is determined according to the following equation Ly , the lateral acceleration command a Lz ; where k L1 , k L2 , k L3 , k L4 , k L5 , k L6 , K Ls1 , K Ls2 , A L , B L are auxiliary variables for simplifying equation description, R' L , θ' LS , are the distance R L , the line-of-sight angle θ LS , the line-of-sight angle deviation of the leading aircraft to the target, the derivative of x L , h L1 , h L2 , h L3 , h L4 , α L1 , α L2 , α L3 , α L4 , q L1 , q L2 are preset approaching law guidance constants, the value range is h L1 > 0, h L2 > 0, h L3 > 0, h L4 > 0, α L1 > 1, 0 < α L2 < 1, α L3 > 1, 0 < α L4 < 1, q L1 > 0, q L2 > 0; According to the normal acceleration command a Ly , the lateral acceleration command a Lz controls the motion state of the lead aircraft itself.

2. A method of multi-air vehicle cooperative terminal guidance with a line-of-sight separation angle constraint, applied to a slave air vehicle in a multi-air vehicle, wherein, The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: Determine the status information of both the slave and leader aircraft. The slave aircraft's status information includes its flight speed V. i At the initial moment of terminal guidance, the distance x from the target to the aircraft iT And the following parameters defined in the aircraft's local inertial coordinate system: line-of-sight tilt angle λ at the initial moment of terminal guidance. i0 x-position at time t i From the aircraft in x i Position velocity lead angle θ i Speed ​​lead angle x i The angle of view θ of the position iS , line of sight deflection From the aircraft in x i Position of the target distance R i The state information of the lead vehicle includes the following parameters defined in the lead vehicle's local inertial coordinate system: the expected line-of-sight deflection η at the end of terminal guidance. Lf The desired line-of-sight tilt angle λ at the end of the final guidance phase. Lf Line-of-sight tilt angle λ at the initial moment of terminal guidance L0 Line-of-sight angle η at the initial moment of terminal guidance L0 Line-of-sight tilt velocity λ' at the initial moment of terminal guidance L0 Line-of-sight deflection angular velocity η' at the initial moment of terminal guidance L0 The state information of the lead vehicle also includes: the line-of-sight tilt angle Θ at the initial moment of terminal guidance, defined in the global inertial coordinate system. LS0 and line of sight deflection Φ LS0 The aircraft's state information also includes: the line-of-sight tilt angle Θ at the initial moment of final guidance, defined in the global inertial coordinate system. iS0 and line of sight deflection Φ iS0 ; According to the state information of the lead aircraft, the command polynomial coefficients a i1 , b i1 , c i1 , d i1 , a i2 , b i2 , c i2 , d i2 are determined from the state information of the lead aircraft and the following equations i0 , the desired line-of-sight angle velocity λ' i0 , the line-of-sight angle velocity η' i0 , the desired line-of-sight angle η if at the end of the terminal guidance at the initial time defined in the local inertial coordinate system of the lead aircraft c θi = -sin Θ iS0 cos Φ iS0 cos Θ LS0 cos Φ LS0 + cos Θ iS0 sin Θ LS0 - sin Θ iS0 sin Φ iS0 cos Θ LS0 sin Φ LS0 c θL = -sin Θ LS0 cos Φ LS0 cos Θ iS0 cos Φ iS0 + cos Θ LS0 sin Θ iS0 - sin Θ LS0 sin Θ LS0 cos Θ iS0 sin Φ iS0 where λ if is the desired line-of-sight angle at the end of the terminal guidance defined in the local inertial frame of the aircraft, c θi , c θL , is an auxiliary variable to simplify the equation description, T go is the desired flight time at the end of the terminal guidance phase; The line-of-sight angle tracking error x i1 , the line-of-sight angle velocity tracking error x i2 , the line-of-sight angle tracking error x i3 , the line-of-sight angle velocity tracking error x i4 , the line-of-sight angle tracking error x i1 , the line-of-sight angle velocity tracking error x i2 : where; k i0 For the convenience of calculation, the intermediate variable, l i1 , l i2 , l i3 , l i4 , m i1 , m i2 , m i3 , m i4 , p i1 , p i2 is the preset sliding mode surface guidance constant, the value range is l i1 > 0, l i2 > 0, l i3 > 0, l i4 > 0, m i1 > 1, 0 < m i2 < 1, m i3 > 1, 0 < m i4 < 1, p i1 > 0, p i2 > 0, sign m (·) = sign (·) |·| m is the sign function with index; The normal acceleration command a iy from the aircraft is determined according to the following equation iz ; where k i1 , k i2 , k i3 , k i4 , k i5 , k i6 , K is1 , K is2 , A i , B i are auxiliary variables for simplifying equation description, R' i , θ' iS , are the distance R i , the line-of-sight angle θ iS , the line-of-sight angle deviation , the derivative of the line-of-sight angle deviation with respect to x i , h i1 , h i2 , h i3 , h i4 , α i1 , α i2 , α i3 , α i4 , q i1 , q i2 are preset approaching law guidance constants, and the value ranges are h i1 > 0, h i2 > 0, h i3 > 0, h i4 > 0, α i1 > 1, 0 < α i2 < 1, α i3 > 1, 0 < α i4 < 1, q i1 > 0, q i2 > 0. According to the normal acceleration command a iy , the lateral acceleration command a iz control the motion state of the aircraft itself.

3. A multi-aircraft system, characterized by, The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises:

4. A program product, characterized by The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises:

5. An aircraft, characterized in that The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft, and the method comprises: The multi-aircraft includes a lead aircraft and at least one follower aircraft

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